Skip to main content
Fachgebiete
Automobil + Motoren Bauwesen + Immobilien Business IT + Informatik Elektrotechnik + Elektronik Energie + Nachhaltigkeit Finance + Banking Management + Führung Marketing + Vertrieb Maschinenbau + Werkstoffe Versicherung + Risiko
DE
EN
Bücher
Zeitschriften
Themenseiten
Organisationspsychologie Projektmanagement Marketing Smart Manufacturing
Weitere Formate
Podcasts Webinare Technik Webinare Wirtschaft Kongresse Veranstaltungskalender Awards
Jetzt Einzelzugang starten
Zugang für Unternehmen
Referenzkunden
SLX-Digitalkonferenz: Zukunftswerkstatt 2024

Mehr Umsatz mit Top-Kontakten

Am 7. Mai erfahren Sie, wie Vertriebsteams Leadgenerierung, Leadnurturing und Leadstrategien effizient steuern können.
Erweiterte Suche
Anmelden
nach oben
Erschienen in:
Fluid Flow Modeling Kapitel lesen Erstes Kapitel lesen

2017 | OriginalPaper | Buchkapitel

12. Bibliographical Remarks

verfasst von : Eduard Feireisl, Antonín Novotný

Erschienen in: Singular Limits in Thermodynamics of Viscous Fluids

Verlag: Springer International Publishing

Einloggen

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config
loading …

Abstract

The material collected in Chapter 1 is standard. We refer to the classical monographs by Batchelor [20] or Lamb [180] for the full account on the mathematical theory of continuum fluid mechanics. A more recent treatment may be found in Truesdell and Noll [259] or Truesdell and Rajagopal [260]. An excellent introduction to the mathematical theory of waves in fluids is contained in Lighthill’s book [188].

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

Jetzt informieren
Vorheriges Kapitel Appendix
Literatur
1.
R.A. Adams, Sobolev Spaces (Academic, New York, 1975)MATH
2.
S. Agmon, A. Douglis, L. Nirenberg, Estimates near the boundary for solutions of elliptic partial differential equations. Commun. Pure Appl. Math. 12, 623–727 (1959)MATHCrossRef
3.
T. Alazard, Low Mach number flows and combustion. SIAM J. Math. Anal. 38(4), 1186–1213 (electronic) (2006)
4.
5.
R. Alexandre, C. Villani, On the Boltzmann equation for long-range interactions. Comm. Pure Appl. Math. 55, 30–70 (2002)MathSciNetMATHCrossRef
6.
7.
H. Amann, Nonhomogeneous linear and quasilinear elliptic and parabolic boundary value problems, in Function Spaces, Differential Operators and Nonlinear Analysis (Friedrichroda, 1992). Teubner-Texte zur Mathematik, vol. 133 (Teubner, Stuttgart, 1993), pp. 9–126
8.
9.
A.A. Amirat, D. Bresch, J. Lemoine, J. Simon, Effect of rugosity on a flow governed by stationary Navier-Stokes equations. Q. Appl. Math. 59, 768–785 (2001)MathSciNetMATHCrossRef
10.
A.A. Amirat, E. Climent, E. Fernández-Cara, J. Simon, The Stokes equations with Fourier boundary conditions on a wall with asperities. Math. Models Methods Appl. 24, 255–276 (2001)MathSciNetMATHCrossRef
11.
S.N. Antontsev, A.V. Kazhikhov, V.N. Monakhov, Krajevyje Zadaci Mechaniki Neodnorodnych Zidkostej (Nauka, Novosibirsk, 1983)
12.
D. Azé, Elements d’analyse Fonctionnelle et Variationnelle (Elipses, Paris, 1997)MATH
13.
H. Babovsky, M. Padula, A new contribution to nonlinear stability of a discrete velocity model. Commun. Math. Phys. 144(1), 87–106 (1992)MathSciNetMATHCrossRef
14.
H. Bahouri, J.-Y. Chemin, Équations d’ondes quasilinéaires et effet dispersif. Int. Math. Res. Not. 21, 1141–1178 (1999)MATHCrossRef
15.
16.
C. Bardos, S. Ukai, The classical incompressible Navier-Stokes limit of the Boltzmann equation. Math. Models Methods Appl. Sci. 1(2), 235–257 (1991)MathSciNetMATHCrossRef
17.
C. Bardos, F. Golse, C.D. Levermore, Fluid dynamical limits of kinetic equations, I: formal derivation. J. Stat. Phys. 63, 323–344 (1991)MATH
18.
C. Bardos, F. Golse, C.D. Levermore, Fluid dynamical limits of kinetic equations, II: convergence proofs for the Boltzman equation. Commun. Pure Appl. Math. 46, 667–753 (1993)MATH
19.
C. Bardos, F. Golse, C.D. Levermore, The acoustic limit for the Boltzmann equation. Arch. Ration. Mech. Anal. 153, 177–204 (2000)MathSciNetMATHCrossRef
20.
G.K. Batchelor, An Introduction to Fluid Dynamics (Cambridge University Press, Cambridge, 1967)MATH
21.
A. Battaner, Astrophysical Fluid Dynamics (Cambridge University Press, Cambridge, 1996)CrossRef
22.
E. Becker, Gasdynamik (Teubner-Verlag, Stuttgart, 1966)MATH
23.
H. Beirao da Veiga, An L p theory for the n-dimensional, stationary, compressible Navier-Stokes equations, and incompressible limit for compressible fluids. Commun. Math. Phys. 109, 229–248 (1987)MathSciNetMATHCrossRef
24.
P. Bella, E. Feireisl, A. Novotny, Dimension reduction for compressible viscous fluids. Acta Appl. Math. 134, 111–121 (2014)MathSciNetMATHCrossRef
25.
P. Bella, E. Feireisl, M. Lewicka, A. Novotny, A rigorous justification of the Euler and Navier-Stokes equations with geometric effects. SIAM J. Math. Anal. 48(6) 3907–3930 (2016)MathSciNetMATHCrossRef
26.
S. Benzoni-Gavage, D. Serre, Multidimensional Hyperbolic Partial Differential Equations, First Order Systems and Applications. Oxford Mathematical Monographs (The Clarendon Press/Oxford University Press, Oxford, 2007)MATH
27.
J. Bergh, J. Löfström, Interpolation Spaces. An Introduction (Springer, Berlin, 1976). Grundlehren der Mathematischen Wissenschaften, No. 223
28.
M.E. Bogovskii, Solution of some vector analysis problems connected with operators div and grad (in Russian). Trudy Sem. S.L. Sobolev 80(1), 5–40 (1980)
29.
J. Bolik, W. von Wahl, Estimating ∇u in terms of divu, curlu, either (ν, u) or ν ×u and the topology. Math. Meth. Appl. Sci. 20, 737–744 (1997)
30.
R.E. Bolz, G.L. Tuve (eds.), Handbook of Tables for Applied Engineering Science (CRC Press, Cleveland, 1973)
31.
32.
L. Brandolese, M.E. Schonbek, Large time decay and growth for solutions of a viscous Boussinesq system. Trans. Am. Math. Soc. 364(10), 5057–5090 (2012)MathSciNetMATHCrossRef
33.
34.
D. Bresch, B. Desjardins, Stabilité de solutions faibles globales pour les équations de Navier-Stokes compressibles avec température. C.R. Acad. Sci. Paris 343, 219–224 (2006)
35.
D. Bresch, B. Desjardins, On the existence of global weak solutions to the Navier-Stokes equations for viscous compressible and heat conducting fluids. J. Math. Pures Appl. 87, 57–90 (2007)MathSciNetMATHCrossRef
36.
D. Bresch, P.-E. Jabin, Global existence of weak solutions for compressible Navier-Stokes equations: thermodynamically unstable pressure and anisotropic viscous stress tensor (2015), arxiv preprint No. 1507.04629v1
37.
D. Bresch, B. Desjardins, E. Grenier, C.-K. Lin, Low Mach number limit of viscous polytropic flows: formal asymptotic in the periodic case. Stud. Appl. Math. 109, 125–149 (2002)MathSciNetMATHCrossRef
38.
A. Bressan, Hyperbolic Systems of Conservation Laws. The One Dimensional Cauchy Problem (Oxford University Press, Oxford, 2000)
39.
J. Březina, A. Novotný, On weak solutions of steady Navier-Stokes equations for monatomic gas. Comment. Math. Univ. Carol. 49, 611–632 (2008)MathSciNetMATH
40.
H. Brezis, Operateurs Maximaux Monotones et Semi-Groupes de Contractions Dans Les Espaces de Hilbert (North-Holland, Amsterdam, 1973)MATH
41.
H. Brezis, Analyse Fonctionnelle (Masson, Paris, 1987)MATH
42.
D. Bucur, E. Feireisl, The incompressible limit of the full Navier-Stokes-Fourier system on domains with rough boundaries. Nonlinear Anal. Real World Appl. 10, 3203–3229 (2009)MathSciNetMATHCrossRef
43.
N. Burq, Global Strichartz estimates for nontrapping geometries: about an article by H.F. Smith and C. D. Sogge: “Global Strichartz estimates for nontrapping perturbations of the Laplacian”. Commun. Partial Differ. Equ. 28(9–10), 1675–1683 (2003)
44.
N. Burq, F. Planchon, J.G. Stalker, A.S. Tahvildar-Zadeh, Strichartz estimates for the wave and Schrödinger equations with potentials of critical decay. Indiana Univ. Math. J. 53(6), 1665–1680 (2004)MathSciNetMATHCrossRef
45.
L. Caffarelli, R.V. Kohn, L. Nirenberg, On the regularity of the solutions of the Navier-Stokes equations. Commun. Pure Appl. Math. 35, 771–831 (1982)MATHCrossRef
46.
A.P. Calderón, A. Zygmund, On singular integrals. Am. J. Math. 78, 289–309 (1956)MATHCrossRef
47.
48.
H. Callen, Thermodynamics and an Introduction to Thermostatistics (Wiley, New York, 1985)MATH
49.
R.W. Carroll, Abstract Methods in Partial Differential Equations. Harper’s Series in Modern Mathematics (Harper and Row Publishers, New York, 1969)
50.
J. Casado-Díaz, I. Gayte, The two-scale convergence method applied to generalized Besicovitch spaces. Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 458(2028), 2925–2946 (2002)MathSciNetMATHCrossRef
51.
J. Casado-Díaz, E. Fernández-Cara, J. Simon, Why viscous fluids adhere to rugose walls: a mathematical explanation. J. Differ. Equ. 189, 526–537 (2003)MathSciNetMATHCrossRef
52.
J. Casado-Díaz, M. Luna-Laynez, F.J. Suárez-Grau, Asymptotic behavior of a viscous fluid with slip boundary conditions on a slightly rough wall. Math. Models Methods Appl. Sci. 20, 121–156 (2010)MathSciNetMATHCrossRef
53.
S. Chandrasekhar, Hydrodynamic and Hydrodynamic Stability (Clarendon Press, Oxford, 1961)MATH
54.
T. Chang, B.J. Jin, A. Novotny, Compressible Navier-Stokes system with general inflow-outflow boundary data Preprint (2017)
55.
J.-Y. Chemin, Perfect Incompressible Fluids. Oxford Lecture Series in Mathematics and its Applications, vol. 14 (The Clarendon Press/Oxford University Press, New York, 1998). Translated from the 1995 French original by Isabelle Gallagher and Dragos Iftimie
56.
J.-Y. Chemin, B. Desjardins, I. Gallagher, E. Grenier, Mathematical Geophysics. Oxford Lecture Series in Mathematics and its Applications, vol. 32 (The Clarendon Press/Oxford University Press, Oxford, 2006)
57.
G.-Q. Chen, M. Torres, Divergence-measure fields, sets of finite perimeter, and conservation laws. Arch. Ration. Mech. Anal. 175(2), 245–267 (2005)MathSciNetMATHCrossRef
58.
C.-Q. Chen, D. Wang, The Cauchy problem for the Euler equations for compressible fluids. Handb. Math. Fluid Dyn. 1, 421–543 (2001). North-Holland, Amsterdam
59.
Y. Cho, H.J. Choe, H. Kim, Unique solvability of the initial boundary value problems for compressible viscous fluids. J. Math. Pures Appl. 83, 243–275 (2004)MathSciNetMATHCrossRef
60.
A.J. Chorin, J.E. Marsden, A Mathematical Introduction to Fluid Mechanics (Springer, New York, 1979)MATHCrossRef
61.
D. Christodoulou, S. Klainerman, Asymptotic properties of linear field equations in Minkowski space. Commun. Pure Appl. Math. 43(2), 137–199 (1990)MathSciNetMATHCrossRef
62.
R. Coifman, Y. Meyer, On commutators of singular integrals and bilinear singular integrals. Trans. Am. Math. Soc. 212, 315–331 (1975)MathSciNetMATHCrossRef
63.
T. Colonius, S.K. Lele, P. Moin, Sound generation in mixing layer. J. Fluid Mech. 330, 375–409 (1997)MATHCrossRef
64.
P. Constantin, A. Debussche, G.P. Galdi, M. Røcircužička, G. Seregin, Topics in Mathematical Fluid Mechanics. Lecture Notes in Mathematics, vol. 2073 (Springer, Heidelberg; Fondazione C.I.M.E., Florence, 2013). Lectures from the CIME Summer School held in Cetraro, September 2010, Edited by Hugo Beirão da Veiga and Franco Flandoli, Fondazione CIME/CIME Foundation Subseries
65.
66.
H.L. Cycon, R.G. Froese, W. Kirsch, B. Simon, Schrödinger Operators: With Applications to Quantum Mechanics and Global Geometry. Texts and Monographs in Physics (Springer, Berlin/Heidelberg, 1987)
67.
68.
C.M. Dafermos, Hyperbolic Conservation Laws in Continuum Physics (Springer, Berlin, 2000)MATHCrossRef
69.
70.
R. Danchin, Global existence in critical spaces for compressible Navier-Stokes equations. Invent. Math. 141, 579–614 (2000)MathSciNetMATHCrossRef
71.
R. Danchin, Global existence in critical spaces for flows of compressible viscous and heat-conductive gases. Arch. Ration. Mech. Anal. 160(1), 1–39 (2001)MathSciNetMATHCrossRef
72.
R. Danchin, Low Mach number limit for viscous compressible flows. M2AN Math. Model Numer. Anal. 39, 459–475 (2005)
73.
R. Danchin, The inviscid limit for density-dependent incompressible fluids. Ann. Fac. Sci. Toulouse Math. (6) 15(4), 637–688 (2006)
74.
R. Danchin, M. Paicu, Existence and uniqueness results for the Boussinesq system with data in Lorentz spaces. Phys. D 237(10–12), 1444–1460 (2008)MathSciNetMATHCrossRef
75.
R. Danchin, M. Paicu, Global well-posedness issues for the inviscid Boussinesq system with Yudovich’s type data. Commun. Math. Phys. 290(1), 1–14 (2009)MathSciNetMATHCrossRef
76.
R. Danchin, M. Paicu, Global existence results for the anisotropic Boussinesq system in dimension two. Math. Models Methods Appl. Sci. 21(3), 421–457 (2011)MathSciNetMATHCrossRef
77.
R. Denk, M. Hieber, J. Prüss, R-boundedness, Fourier multipliers and problems of elliptic and parabolic type. Mem. Am. Math. Soc. 166(788), 3 (2003)
78.
R. Denk, M. Hieber, J. Prüss, Optimal L p − L q -estimates for parabolic boundary value problems with inhomogeneous data. Math. Z. 257, 193–224 (2007)MathSciNetMATHCrossRef
79.
B. Desjardins, Regularity of weak solutions of the compressible isentropic Navier-Stokes equations. Commun. Partial Differ. Equ. 22, 977–1008 (1997)MathSciNetMATHCrossRef
80.
B. Desjardins, E. Grenier, Low Mach number limit of viscous compressible flows in the whole space. Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 455(1986), 2271–2279 (1999)MathSciNetMATHCrossRef
81.
B. Desjardins, E. Grenier, P.-L. Lions, N. Masmoudi, Incompressible limit for solutions of the isentropic Navier-Stokes equations with Dirichlet boundary conditions. J. Math. Pures Appl. 78, 461–471 (1999)MathSciNetMATHCrossRef
82.
83.
84.
85.
R.J. DiPerna, P.-L. Lions, Ordinary differential equations, transport theory and Sobolev spaces. Invent. Math. 98, 511–547 (1989)MathSciNetMATHCrossRef
86.
R.J. DiPerna, A. Majda, Reduced Hausdorff dimension and concentration cancellation for two-dimensional incompressible flow. J. Am. Math. Soc. 1, 59–95 (1988)MathSciNetMATH
87.
B. Ducomet, E. Feireisl, A regularizing effect of radiation in the equations of fluid dynamics. Math. Methods Appl. Sci. 28, 661–685 (2005)MathSciNetMATHCrossRef
88.
W. E, Boundary layer theory and the zero-viscosity limit of the Navier-Stokes equation. Acta Math. Sinica (Engl. Ser.) 16, 207–218 (2000)
89.
D.B. Ebin, The motion of slightly compressible fluids viewed as a motion with strong constraining force. Ann. Math. 105, 141–200 (1977)MathSciNetMATHCrossRef
90.
R.E. Edwards, Functional Analysis (Holt-Rinehart-Winston, New York, 1965)MATH
91.
D.M. Eidus, Limiting amplitude principle (in Russian). Usp. Mat. Nauk 24(3), 91–156 (1969)
92.
I. Ekeland, R. Temam, Convex Analysis and Variational Problems (North-Holland, Amsterdam, 1976)MATH
93.
S. Eliezer, A. Ghatak, H. Hora, An Introduction to Equations of States, Theory and Applications (Cambridge University Press, Cambridge, 1986)MATH
94.
B.O. Enflo, C.M. Hedberg, Theory of Nonlinear Acoustics in Fluids (Kluwer Academic Publishers, Dordrecht, 2002)MATH
95.
L.C. Evans, Weak Convergence Methods for Nonlinear Partial Differential Equations (American Mathematical Society, Providence, 1990)CrossRef
96.
L.C. Evans, Partial Differential Equations. Graduate Studies in Mathematics, vol. 19 (American Mathematical Society, Providence, 1998)
97.
L.C. Evans, R.F. Gariepy, Measure Theory and Fine Properties of Functions (CRC Press, Boca Raton, 1992)MATH
98.
R. Eymard, T. Gallouet, R. herbin, J.C. Latché, A convergent finite element- finite volume scheme for compressible Stokes equations. The isentropic case. Math. Comput. 79, 649–675 (2010)
99.
R. Farwig, H. Kozono, H. Sohr, An L q -approach to Stokes and Navier-Stokes equations in general domains. Acta Math. 195, 21–53 (2005)MathSciNetMATHCrossRef
100.
C.L. Fefferman, Existence and smoothness of the Navier-Stokes equation, in The Millennium Prize Problems (Clay Mathematics Institute, Cambridge, 2006), pp. 57–67MATH
101.
E. Feireisl, On compactness of solutions to the compressible isentropic Navier-Stokes equations when the density is not square integrable. Comment. Math. Univ. Carol. 42(1), 83–98 (2001)MathSciNetMATH
102.
E. Feireisl, Dynamics of Viscous Compressible Fluids (Oxford University Press, Oxford, 2004)MATH
103.
E. Feireisl, On the motion of a viscous, compressible, and heat conducting fluid. Indiana Univ. Math. J. 53, 1707–1740 (2004)MathSciNetCrossRef
104.
E. Feireisl, Mathematics of viscous, compressible, and heat conducting fluids, in Contemporary Mathematics, ed. by G.-Q. Chen, G. Gasper, J. Jerome, vol. 371 (American Mathematical Society, Providence, 2005), pp. 133–151
105.
E. Feireisl, Stability of flows of real monatomic gases. Commun. Partial Differ. Equ. 31, 325–348 (2006)MATHCrossRef
106.
E. Feireisl, Relative entropies in thermodynamics of complete fluid systems. Discrete Contin. Dyn. Syst. 32(9), 3059–3080 (2012)MathSciNetMATHCrossRef
107.
E. Feireisl, A. Novotný, On a simple model of reacting compressible flows arising in astrophysics. Proc. R. Soc. Edinb. A 135, 1169–1194 (2005)MathSciNetMATHCrossRef
108.
E. Feireisl, A. Novotný, The Oberbeck-Boussinesq approximation as a singular limit of the full Navier-Stokes-Fourier system. J. Math. Fluid Mech. 11(2), 274–302 (2009)MathSciNetMATHCrossRef
109.
E. Feireisl, A. Novotný, On the low Mach number limit for the full Navier-Stokes-Fourier system. Arch. Ration. Mech. Anal. 186, 77–107 (2007)MathSciNetMATHCrossRef
110.
E. Feireisl, A. Novotný, Weak-strong uniqueness property for the full Navier-Stokes-Fourier system. Arch. Ration. Mech. Anal. 204, 683–706 (2012)MathSciNetMATHCrossRef
111.
E. Feireisl, A. Novotný, Inviscid incompressible limits of the full Navier-Stokes-Fourier system. Commun. Math. Phys. 321, 605–628 (2013)MathSciNetMATHCrossRef
112.
E. Feireisl, A. Novotný, Inviscid incompressible limits under mild stratification: a rigorous derivation of the Euler-Boussinesq system. Appl. Math. Optim. 70, 279–307 (2014)MathSciNetMATHCrossRef
113.
E. Feireisl, A. Novotny, Multiple scales and singular limits for compressible rotating fluids with general initial data. Commun. Partial Differ. Equ. 39, 1104–1127 (2014)MathSciNetMATHCrossRef
114.
115.
E. Feireisl, A. Novotný, Stationary Solutions to the Compressible Navier-Stokes System with General Boundary Conditions. Preprint Nečas Center for Mathematical Modeling (Charles University, Prague, 2017)
116.
E. Feireisl, Š. Matuš˚u Nečasová, H. Petzeltová, I. Straškraba, On the motion of a viscous compressible fluid driven by a time-periodic external force. Arch Ration. Mech. Anal. 149, 69–96 (1999)
117.
E. Feireisl, A. Novotný, H. Petzeltová, On the existence of globally defined weak solutions to the Navier-Stokes equations of compressible isentropic fluids. J. Math. Fluid Mech. 3, 358–392 (2001)MathSciNetMATHCrossRef
118.
E. Feireisl, J. Málek, A. Novotný, Navier’s slip and incompressible limits in domains with variable bottoms. Discrete Contin. Dyn. Syst. Ser. S 1, 427–460 (2008)MathSciNetMATHCrossRef
119.
E. Feireisl, A. Novotný, Y. Sun, Suitable weak solutions to the Navier-Stokes equations of compressible viscous fluids. Indiana Univ. Math. J. 60, 611–632 (2011)MathSciNetMATHCrossRef
120.
E. Feireisl, B.J. Jin, A. Novotný, Relative entropies, suitable weak solutions, and weak-strong uniqueness for the compressible Navier-Stokes system. J. Math. Fluid Mech. 14(4), 717–730 (2012)MathSciNetMATHCrossRef
121.
E. Feireisl, P. Mucha, A. Novotny, M. Pokorný, Time-periodic solutions to the full Navier-Stokes-Fourier system Arch. Ration. Mech. Anal. 204(3), 745–786 (2012)MathSciNetMATHCrossRef
122.
E. Feireisl, T. Karper, O. Kreml, J. Stebel, Stability with respect to domain of the low Mach number limit of compressible viscous fluids. Math. Models Methods Appl. Sci. 23(13), 2465–2493 (2013)MathSciNetMATHCrossRef
123.
E. Feireisl, A. Novotný, Y. Sun, Dissipative solutions and the incompressible inviscid limits of the compressible magnetohydrodynamics system in unbounded domains. Discrete Contin. Dyn. Syst. 34, 121–143 (2014)MathSciNetMATHCrossRef
124.
E. Feireisl, T. Karper, A. Novotny, A convergent mixed numerical method for the Navier-Stokes-Fourier system. IMA J. Numer. Anal. 36, 1477–1535 (2016)MathSciNetCrossRef
125.
E. Feireisl, T. Karper, M. Pokorny, Mathematical Theory of Compressible Viscous Fluids – Analysis and Numerics (Birkhauser, Boston, 2016)MATHCrossRef
126.
127.
128.
J. Frehse, S. Goj, M. Steinhauer, L p – estimates for the Navier-Stokes equations for steady compressible flow. Manuscripta Math. 116, 265–275 (2005)MathSciNetMATHCrossRef
129.
J.B. Freud, S.K. Lele, M. Wang, Computational prediction of flow-generated sound. Ann. Rev. Fluid Mech. 38, 483–512 (2006)MathSciNetCrossRef
130.
H. Gajewski, K. Gröger, K. Zacharias, Nichtlineare Operatorgleichungen und Operatordifferentialgleichungen. (Akademie, Berlin, 1974)
131.
G.P. Galdi, An Introduction to the Mathematical Theory of the Navier – Stokes Equations, I (Springer, New York, 1994)MATH
132.
G. Gallavotti, Statistical Mechanics: A Short Treatise (Springer, Heidelberg, 1999)MATHCrossRef
133.
T. Gallouët, R. Herbin, D. Maltese, A. Novotny, Error estimates for a numerical approximation to the compressible barotropic navier–stokes equations. IMA J. Numer. Anal. 36(2), 543–592 (2016)MathSciNetCrossRef
134.
M. Geißert, H. Heck, M. Hieber, On the equation div u = g and Bogovskiĭ’s operator in Sobolev spaces of negative order, in Partial Differential Equations and Functional Analysis. Operator Theory: Advances and Applications, vol. 168 (Birkhäuser, Basel, 2006), pp. 113–121
135.
G. Geymonat, P. Grisvard, Alcuni risultati di teoria spettrale per i problemi ai limiti lineari ellittici. Rend. Sem. Mat. Univ. Padova 38, 121–173 (1967)MathSciNetMATH
136.
D. Gilbarg, N. Trudinger, Elliptic Partial Differential Equations of Second Order (Springer, Berlin, 1983)MATHCrossRef
137.
A.E. Gill, Atmosphere-Ocean Dynamics (Academic, San Diego, 1982)
138.
P.A. Gilman, G.A. Glatzmaier, Compressible convection in a rotating spherical shell. I. Anelastic equations. Astrophys. J. Suppl. 45(2), 335–349 (1981)MathSciNetCrossRef
139.
V. Girinon, Navier-Stokes equations with nonhomogeneous boundary conditions in a bounded three-dimensional domain. J. Math. Fluid Mech. 13, 309–339 (2011)MathSciNetMATHCrossRef
140.
G.A. Glatzmaier, P.A. Gilman, Compressible convection in a rotating spherical shell. II. A linear anelastic model. Astrophys. J. Suppl. 45(2), 351–380 (1981)MathSciNet
141.
F. Golanski, V. Fortuné, E. Lamballais, Noise radiated by a non-isothermal temporal mixing layer, II. Prediction using DNS in the framework of low Mach number approximation. Theor. Comput. Fluid Dyn. 19, 391–416 (2005)MATH
142.
F. Golanski, C. Moser, L. Nadai, C. Pras, E. Lamballais, Numerical methodology for the computation of the sound generated by a non-isothermal mixing layer at low Mach number, in Direct and Large Eddy Simulation, VI, ed. by E. Lamballais, R. Freidrichs, R. Geurts, B.J. Métais (Springer, Heidelberg, 2006)
143.
F. Golse, C.D. Levermore, The Stokes-Fourier and acoustic limits for the Boltzmann equation. Commun. Pure Appl. Math. 55, 336–393 (2002)MathSciNetMATHCrossRef
144.
F. Golse, L. Saint-Raymond, The Navier-Stokes limit of the Boltzmann equation for bounded collision kernels. Invent. Math. 155, 81–161 (2004)MathSciNetMATHCrossRef
145.
D. Gough, The anelastic approximation for thermal convection. J. Atmos. Sci. 26, 448–456 (1969)CrossRef
146.
E. Grenier, Y. Guo, T.T. Nguyen, Spectral stability of Prandtl boundary layers: an overview. Analysis (Berlin) 35(4), 343–355 (2015)
147.
T. Hagstrom, J. Lorenz, On the stability of approximate solutions of hyperbolic-parabolic systems and all-time existence of smooth, slightly compressible flows. Indiana Univ. Math. J. 51, 1339–1387 (2002)MathSciNetMATHCrossRef
148.
M. Hieber, J. Prüss, Heat kernels and maximal L p -L q estimates for parabolic evolution equations. Commun. Partial Differ. Equ. 22(9,10), 1647–1669 (1997)
149.
D. Hoff, Global existence for 1D compressible, isentropic Navier-Stokes equations with large initial data. Trans. Am. Math. Soc. 303, 169–181 (1987)MATH
150.
D. Hoff, Spherically symmetric solutions of the Navier-Stokes equations for compressible, isothermal flow with large, discontinuous initial data. Indiana Univ. Math. J. 41, 1225–1302 (1992)MathSciNetMATHCrossRef
151.
D. Hoff, Global solutions of the Navier-Stokes equations for multidimensional compressible flow with discontinuous initial data. J. Differ. Equ. 120, 215–254 (1995)MathSciNetMATHCrossRef
152.
D. Hoff, Strong convergence to global solutions for multidimensional flows of compressible, viscous fluids with polytropic equations of state and discontinuous initial data. Arch. Ration. Mech. Anal. 132, 1–14 (1995)MathSciNetMATHCrossRef
153.
D. Hoff, Discontinuous solutions of the Navier-Stokes equations for multidimensional flows of heat conducting fluids. Arch. Ration. Mech. Anal. 139, 303–354 (1997)MathSciNetMATHCrossRef
154.
D. Hoff, Dynamics of singularity surfaces for compressible viscous flows in two space dimensions. Commun. Pure Appl. Math. 55, 1365–1407 (2002)MathSciNetMATHCrossRef
155.
D. Hoff, D. Serre, The failure of continuous dependence on initial data for the Navier-Stokes equations of compressible flow. SIAM J. Appl. Math. 51, 887–898 (1991)MathSciNetMATHCrossRef
156.
157.
158.
W. Jaeger, A. Mikelić, On the roughness-induced effective boundary conditions for an incompressible viscous flow. J. Differ. Equ. 170, 96–122 (2001)MathSciNetMATHCrossRef
159.
S. Jiang, Global solutions of the Cauchy problem for a viscous, polytropic ideal gas. Ann. Sc. Norm. Super. Pisa 26, 47–74 (1998)MathSciNetMATH
160.
S. Jiang, C. Zhou, Existence of weak solutions to the three dimensional steady compressible Navier–Stokes equations. Ann. IHP: Anal. Nonlinéaire 28, 485–498 (2011)MathSciNetMATH
161.
S. Jiang, Q. Ju, F. Li, Incompressible limit of the compressible magnetohydrodynamic equations with periodic boundary conditions. Commun. Math. Phys. 297(2), 371–400 (2010)MathSciNetMATHCrossRef
162.
F. John, Nonlinear Wave Equations, Formation of Singularities. University Lecture Series, vol. 2 (American Mathematical Society, Providence, 1990). Seventh Annual Pitcher Lectures delivered at Lehigh University, Bethlehem, Pennsylvania, April 1989
163.
T.K. Karper, A convergent FEM-DG method for the compressible Navier–Stokes equations. Numer. Math. 125(3), 441–510 (2013)MathSciNetMATHCrossRef
164.
T. Kato, On classical solutions of the two-dimensional nonstationary Euler equation. Arch. Ration. Mech. Anal. 25, 188–200 (1967)MathSciNetMATHCrossRef
165.
166.
T. Kato, Remarks on the zero viscosity limit for nonstationary Navier–Stokes flows with boundary, in Seminar on PDE’s, ed. by S.S. Chern (Springer, New York, 1984)
167.
168.
169.
J.L. Kelley, General Topology (Van Nostrand, Inc., Princeton, 1957)MATH
170.
S. Klainerman, A. Majda, Singular limits of quasilinear hyperbolic systems with large parameters and the incompressible limit of compressible fluids. Commun. Pure Appl. Math. 34, 481–524 (1981)MathSciNetMATHCrossRef
171.
R. Klein, Asymptotic analyses for atmospheric flows and the construction of asymptotically adaptive numerical methods. Z. Angw. Math. Mech. 80, 765–777 (2000)MathSciNetMATHCrossRef
172.
R. Klein, Multiple spatial scales in engineering and atmospheric low Mach number flows. ESAIM: Math. Mod. Numer. Anal. 39, 537–559 (2005)MathSciNetMATHCrossRef
173.
R. Klein, N. Botta, T. Schneider, C.D. Munz, S. Roller, A. Meister, L. Hoffmann, T. Sonar, Asymptotic adaptive methods for multi-scale problems in fluid mechanics. J. Eng. Math. 39, 261–343 (2001)MathSciNetMATHCrossRef
174.
G. Kothe, Topological Vector Spaces I (Springer, Heidelberg, 1969)MATH
175.
A. Kufner, O. John, S. Fučík, Function Spaces (Noordhoff International Publishing, Leyden, 1977). Monographs and Textbooks on Mechanics of Solids and Fluids; Mechanics: Analysis
176.
P. Kukučka, On the existence of finite energy weak solutions to the Navier-Stokes equations in irregular domains. Math. Methods Appl. Sci. 32(11), 1428–1451 (2009)MathSciNetMATHCrossRef
177.
O.A. Ladyzhenskaya, The Mathematical Theory of Viscous Incompressible Flow (Gordon and Breach, New York, 1969)MATH
178.
O.A. Ladyzhenskaya, N.N. Uralceva, Equations aux dérivées partielles de type elliptique (Dunod, Paris, 1968)MATH
179.
O.A. Ladyzhenskaya, V.A. Solonnikov, N.N. Uralceva, Linear and Quasilinear Equations of Parabolic Type. Translations of Mathematical Monographs, vol. 23 (American Mathematical Society, Providence, 1968)
180.
H. Lamb, Hydrodynamics (Cambridge University Press, Cambridge, 1932)MATH
181.
182.
H. Leinfelder, A geometric proof of the spectral theorem for unbounded selfadjoint operators. Math. Ann. 242(1), 85–96 (1979)MathSciNetMATHCrossRef
183.
R. Leis, Initial-Boundary Value Problems in Mathematical Physics (B.G. Teubner, Stuttgart, 1986)MATHCrossRef
184.
185.
186.
187.
J. Lighthill, On sound generated aerodynamically II. General theory. Proc. R. Soc. Lond. A 222, 1–32 (1954)MATHCrossRef
188.
J. Lighthill, Waves in Fluids (Cambridge University Press, Cambridge, 1978)MATH
189.
F. Lignières, The small-Péclet-number approximation in stellar radiative zones. Astron. Astrophys. 348, 933–939 (1999)
190.
J.-L. Lions, Quelques remarques sur les problèmes de Dirichlet et de Neumann. Séminaire Jean Leray 6, 1–18 (1961/1962)
191.
P.-L. Lions, Mathematical Topics in Fluid Dynamics, Vol. 1, Incompressible Models (Oxford Science Publication, Oxford, 1996)
192.
P.-L. Lions, Mathematical Topics in Fluid Dynamics, Vol. 2, Compressible Models (Oxford Science Publication, Oxford, 1998)
193.
J.-L. Lions, E. Magenes, Problèmes aux limites non homogènes et applications, I. - III. (Dunod/Gautthier, Villars/Paris, 1968)
194.
P.-L. Lions, N. Masmoudi, Incompressible limit for a viscous compressible fluid. J. Math. Pures Appl. 77, 585–627 (1998)MathSciNetMATHCrossRef
195.
196.
P.-L. Lions, N. Masmoudi, From Boltzmann equations to incompressible fluid mechanics equations, I. Arch. Ration. Mech. Anal. 158, 173–193 (2001)MATHCrossRef
197.
P.-L. Lions, N. Masmoudi, From Boltzmann equations to incompressible fluid mechanics equations, II. Arch. Ration. Mech. Anal. 158, 195–211 (2001)MATHCrossRef
198.
F.B. Lipps, R.S. Hemler, A scale analysis of deep moist convection and some related numerical calculations. J. Atmos. Sci. 39, 2192–2210 (1982)CrossRef
199.
A. Lunardi, Analytic Semigroups and Optimal Regularity in Parabolic Problems (Birkhäuser, Berlin, 1995)MATHCrossRef
200.
A. Majda, Introduction to PDE’s and Waves for the Atmosphere and Ocean. Courant Lecture Notes in Mathematics, vol. 9 (Courant Institute, New York, 2003)
201.
J. Málek, J. Nečas, M. Rokyta, M. R˚užička, Weak and Measure-Valued Solutions to Evolutionary PDE’s (Chapman and Hall, London, 1996)
202.
203.
N. Masmoudi, Incompressible inviscid limit of the compressible Navier–Stokes system. Ann. Inst. Henri Poincaré, Anal. Nonlinéaire 18, 199–224 (2001)
204.
N. Masmoudi, Examples of singular limits in hydrodynamics, in Handbook of Differential Equations, III, ed. by C. Dafermos, E. Feireisl (Elsevier, Amsterdam, 2006)
205.
206.
A. Matsumura, T. Nishida, The initial value problem for the equations of motion of viscous and heat-conductive gases. J. Math. Kyoto Univ. 20, 67–104 (1980)MathSciNetMATHCrossRef
207.
A. Matsumura, T. Nishida, The initial value problem for the equations of motion of compressible and heat conductive fluids. Commun. Math. Phys. 89, 445–464 (1983)MathSciNetMATHCrossRef
208.
A. Matsumura, M. Padula, Stability of stationary flow of compressible fluids subject to large external potential forces. Stab. Appl. Anal. Continuous Media 2, 183–202 (1992)
209.
210.
J. Metcalfe, D. Tataru, Global parametrices and dispersive estimates for variable coefficient wave equations. Math. Ann. 353(4), 1183–1237 (2012)MathSciNetMATHCrossRef
211.
G. Métivier, Small Viscosity and Boundary Layer Methods (Birkhäuser, Basel, 2004)MATHCrossRef
212.
G. Métivier, S. Schochet, The incompressible limit of the non-isentropic Euler equations. Arch. Ration. Mech. Anal. 158, 61–90 (2001)MathSciNetMATHCrossRef
213.
B. Mihalas, B. Weibel-Mihalas, Foundations of Radiation Hydrodynamics (Dover Publications, Dover, 1984)MATH
214.
B.E. Mitchell, S.K. Lele, P. Moin, Direct computation of the sound generated by vortex pairing in an axisymmetric jet. J. Fluid Mech. 383, 113–142 (1999)MATHCrossRef
215.
B. Mohammadi, O. Pironneau, F. Valentin, Rough boundaries and wall laws. Int. J. Numer. Meth. Fluids 27, 169–177 (1998)MathSciNetMATHCrossRef
216.
C.B. Morrey, L. Nirenberg, On the analyticity of the solutions of linear elliptic systems of partial differential equations. Commun. Pure Appl. Math. 10, 271–290 (1957)MathSciNetMATHCrossRef
217.
I. Müller, T. Ruggeri, Rational Extended Thermodynamics. Springer Tracts in Natural Philosophy, vol. 37 (Springer, Heidelberg, 1998)
218.
F. Murat, Compacité par compensation. Ann. Sc. Norm. Sup. Pisa Cl. Sci. Ser. 5 IV, 489–507 (1978)
219.
J. Nečas, Les méthodes directes en théorie des équations elliptiques (Academia, Praha, 1967)MATH
220.
G. Nguetseng, A general convergence result for a functional related to the theory of homogenization. SIAM J. Math. Anal. 20, 608–623 (1989)MathSciNetMATHCrossRef
221.
A. Novotný, M. Padula, L p approach to steady flows of viscous compressible fluids in exterior domains. Arch. Ration. Mech. Anal. 126, 243–297 (1998)MathSciNetMATHCrossRef
222.
A. Novotný, K. Pileckas, Steady compressible Navier-Stokes equations with large potential forces via a method of decomposition. Math. Meth. Appl. Sci. 21, 665–684 (1998)MathSciNetMATHCrossRef
223.
A. Novotný, M. Pokorný, Steady compressible Navier–Stokes–Fourier system for monoatomic gas and its generalizations. J. Differ. Equ. 251, 270–315 (2011)MathSciNetMATHCrossRef
224.
A. Novotný, I. Straškraba, Introduction to the Mathematical Theory of Compressible Flow (Oxford University Press, Oxford, 2004)MATH
225.
Y. Ogura, M. Phillips, Scale analysis for deep and shallow convection in the atmosphere. J. Atmos. Sci. 19, 173–179 (1962)CrossRef
226.
C. Olech, The characterization of the weak* closure of certain sets of integrable functions. SIAM J. Control 12, 311–318 (1974). Collection of articles dedicated to the memory of Lucien W. Neustadt
227.
H.C. Öttinger, Beyond Equilibrium Thermodynamics (Wiley, New Jersey, 2005)CrossRef
228.
J. Oxenius, Kinetic Theory of Particles and Photons (Springer, Berlin, 1986)CrossRef
229.
M. Padula, M. Pokorný, Stability and decay to zero of the L 2-norms of perturbations to a viscous compressible heat conductive fluid motion exterior to a ball. J. Math. Fluid Mech. 3(4), 342–357 (2001)MathSciNetMATHCrossRef
230.
231.
P. Pedregal, Parametrized Measures and Variational Principles (Birkhäuser, Basel, 1997)MATHCrossRef
232.
P.I. Plotnikov, J. Sokolowski, Concentrations of stationary solutions to compressible Navier-Stokes equations. Commun. Math. Phys. 258, 567–608 (2005)MATHCrossRef
233.
P.I. Plotnikov, J. Sokolowski, Stationary solutions of Navier-Stokes equations for diatomic gases. Russ. Math. Surv. 62, 3 (2007)MathSciNetMATHCrossRef
234.
P.I. Plotnikov, W. Weigant, Isothermal Navier-Stokes equations and Radon transform. SIAM J. Math. Anal. 47(1), 626–653 (2015)MathSciNetMATHCrossRef
235.
N.V. Priezjev, S.M. Troian, Influence of periodic wall roughness on the slip behaviour at liquid/solid interfaces: molecular versus continuum predictions. J. Fluid Mech. 554, 25–46 (2006)MATHCrossRef
236.
T. Qian, X.-P. Wang, P. Sheng, Hydrodynamic slip boundary condition at chemically patterned surfaces: a continuum deduction from molecular dynamics. Phys. Rev. E 72, 022501 (2005)CrossRef
237.
M. Reed, B. Simon, Methods of Modern Mathematical Physics. III. Analysis of Operators (Academic/Harcourt Brace Jovanovich Publishers, New York, 1978)
238.
M. Reed, B. Simon, Methods of Modern Mathematical Physics. IV. Analysis of Operators (Academic/Harcourt Brace Jovanovich Publishers, New York, 1978)
239.
W. Rudin, Real and Complex Analysis (McGraw-Hill, Singapore, 1987)MATH
240.
L. Saint-Raymond, Hydrodynamic limits: some improvements of the relative entropy method. Ann. Inst. Henri Poincaré, Anal. Nonlinéaire 26, 705–744 (2009)
241.
R. Salvi, I. Straškraba, Global existence for viscous compressible fluids and their behaviour as t → ∞. J. Fac. Sci. Univ. Tokyo 40(1), 17–52 (1993)
242.
243.
M.E. Schonbek, Large time behaviour of solutions to the Navier-Stokes equations. Commun. Partial Differ. Equ. 11(7), 733–763 (1986)MathSciNetMATHCrossRef
244.
M.E. Schonbek, Lower bounds of rates of decay for solutions to the Navier-Stokes equations. J. Am. Math. Soc. 4(3), 423–449 (1991)MathSciNetMATHCrossRef
245.
M.E. Schonbek, Asymptotic behavior of solutions to the three-dimensional Navier-Stokes equations. Indiana Univ. Math. J. 41(3), 809–823 (1992)MathSciNetMATHCrossRef
246.
247.
D. Serre, Systems of Conservations Laws (Cambridge university Press, Cambridge, 1999)CrossRef
248.
C. Simader, H. Sohr, A new approach to the Helmholtz decomposition and the Neumann problem in Lq-spaces for bounded and exterior domains, in Mathematical Problems Relating to the Navier-Stokes Equations, Series: Advanced in Mathematics for Applied Sciences, ed. by G.P. Galdi (World Scientific, Singapore, 1992), pp. 1–35
249.
H.F. Smith, C.D. Sogge, Global Strichartz estimates for nontrapping perturbations of the Laplacian. Comm. Partial Differ. Equ. 25(11–12), 2171–2183 (2000)MathSciNetMATHCrossRef
250.
H.F. Smith, D. Tataru, Sharp local well-posedness results for the nonlinear wave equation. Ann. Math. (2) 162(1), 291–366 (2005)
251.
E.M. Stein, Singular Integrals and Differential Properties of Functions (Princeton University Press, Princeton, 1970)MATH
252.
253.
F. Sueur, On the inviscid limit for the compressible Navier-Stokes system in an impermeable bounded domain. J. Math. Fluid Mech. 16(1), 163–178 (2014)MathSciNetMATHCrossRef
254.
L. Tartar, Compensated compactness and applications to partial differential equations, in Nonlinear Analysis and Mechanics: Heriot-Watt Symposium, ed. by L.J. Knopps. Research Notes in Mathematics, vol. 39 (Pitman, Boston, 1975), pp. 136–211
255.
R. Temam, Navier-Stokes Equations (North-Holland, Amsterdam, 1977)MATH
256.
R. Temam, Problèmes mathématiques en plasticité (Dunod, Paris, 1986)MATH
257.
H. Triebel, Interpolation Theory, Function Spaces, Differential Operators (VEB Deutscher Verlag der Wissenschaften, Berlin, 1978)MATH
258.
259.
C. Truesdell, W. Noll, The Non-linear Field Theories of Mechanics (Springer, Heidelberg, 2004)MATHCrossRef
260.
C. Truesdell, K.R. Rajagopal, An introduction to the Mechanics of Fluids (Birkhäuser, Boston, 2000)MATHCrossRef
261.
V.A. Vaigant, An example of the nonexistence with respect to time of the global solutions of Navier-Stokes equations for a compressible viscous barotropic fluid (in Russian). Dokl. Akad. Nauk 339(2), 155–156 (1994)MathSciNetMATH
262.
V.A. Vaigant, A.V. Kazhikhov, On the existence of global solutions to two-dimensional Navier-Stokes equations of a compressible viscous fluid (in Russian). Sibirskij Mat. Z. 36(6), 1283–1316 (1995)MATH
263.
B.R. Vaĭnberg, Asimptoticheskie metody v uravneniyakh matematicheskoi fiziki (Moskov Gos University, Moscow, 1982)MATH
264.
A. Valli, M. Zajaczkowski, Navier-Stokes equations for compressible fluids: global existence and qualitative properties of the solutions in the general case. Commun. Math. Phys. 103, 259–296 (1986)MathSciNetMATHCrossRef
265.
A. Vasseur, C. Yu, Existence of global weak solutions for 3D degenerate compressible Navier-Stokes equations. Invent. Math. 206, 935–974 (2016)MathSciNetMATHCrossRef
266.
C. Villani, Limites hydrodynamiques de l’équation de Boltzmann. Astérisque, SMF 282, 365–405 (2002)MATH
267.
M.I. Vishik, L.A. Ljusternik, Regular perturbations and a boundary layer for linear differential equations with a small parameter (in Russian). Usp. Mat. Nauk 12, 3–122 (1957)
268.
269.
A. Visintin, Towards a two-scale calculus. ESAIM Control Optim. Calc. Var. 12(3), 371–397 (electronic) (2006)
270.
W. von Wahl, Estimating ∇u by divu and curlu. Math. Methods Appl. Sci. 15, 123–143 (1992)
271.
S. Wang, S. Jiang, The convergence of the Navier-Stokes-Poisson system to the incompressible Euler equations. Commun. Partial Differ. Equ. 31(4–6), 571–591 (2006)MathSciNetMATHCrossRef
272.
C.H. Wilcox, Sound Propagation in Stratified Fluids. Applied Mathematical Sciences, vol. 50 (Springer, Berlin, 1984)
273.
S.A. Williams, Analyticity of the boundary for Lipschitz domains without Pompeiu property. Indiana Univ. Math. J. 30(3), 357–369 (1981)MathSciNetMATHCrossRef
274.
275.
R.Kh. Zeytounian, Joseph Boussinesq and his approximation: a contemporary view. C.R. Mec. 331, 575–586 (2003)
276.
R.Kh. Zeytounian, Theory and Applications of Viscous Fluid Flows (Springer, Berlin, 2004)MATHCrossRef
277.
Metadaten
Titel
Bibliographical Remarks
verfasst von
Eduard Feireisl
Antonín Novotný
Copyright-Jahr
2017
Buch
Singular Limits in Thermodynamics of Viscous Fluids

Print ISBN: 978-3-319-63780-8

Electronic ISBN: 978-3-319-63781-5

Copyright-Jahr: 2017

DOI
https://doi.org/10.1007/978-3-319-63781-5_12

Premium Partner

    Marktübersichten

    Die im Laufe eines Jahres in der „adhäsion“ veröffentlichten Marktübersichten helfen Anwendern verschiedenster Branchen, sich einen gezielten Überblick über Lieferantenangebote zu verschaffen. 

    Zur Marktübersicht
    Bildnachweise