Skip to main content
Log in

On steady compressible Navier-Stokes equations in plane domains with corners

  • Published:
Mathematische Annalen Aims and scope Submit manuscript

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

References

  1. Beirão da Veiga H.: OnL p-theory for then-dimensional, stationary comparissible Navier-Stokes equations and the incompressible limit for compressible fluids. The equilibrium solutions. Comm. Math. Phys.109 (1987), 229–248

    Google Scholar 

  2. Beirão da Veiga H.: Boundary value problems for a class of first order partial differential equations in Sobolev spaces and applications to the Euler flow, Rend. Sem. Mat. Univ. Padova79 (1988), 247–273

    Google Scholar 

  3. Borchers W., Pileckas K.: Existence, uniqueness and asymptotics of steady jets, Arch. Rat. Mech. Anal.120 (1992), 1–49

    Google Scholar 

  4. Dauge M.: Opérateur de Stokes dans des espaces de Sobolev à points sur des domains anguleux, Can. J. Math.34(4) (1982), 853–882

    Google Scholar 

  5. Dauge M.: Stationary Stokes and Navier-Stokes systems on two and threedimensional domains with corners. Part I.: Linearized Equations, SIAM J. Math. Anal.20(1) (1989), 74–97

    Google Scholar 

  6. Dauge M.: Elliptic boundary value problems on corner domains, smoothness and asymptotics of solutions, Lecture Notes Math.1341 (1988)

  7. Grisvard P.: Singularités des solutions du problème de Stokes dans un polygon, Université de Nice (preprint) (1979)

  8. Grisvard P.: Elliptic problems in nonsmooth domains. Boston, London, Melbourne, Pitman Pub. Co. (1985)

    Google Scholar 

  9. Farwig R.: Stationary solutions of the Navier-Stokes equations with slip boundary conditions, Comm. Part. Diff. Eq.14(11) (1989), 1579–1606

    Google Scholar 

  10. Kellog R.B., Osborn J.E.: A regularity result for the Stokes problem in a convex polygon, J. Funct. Anal.21 (1976), 397–431

    Google Scholar 

  11. Kondrat'ev V.: Boundary value problems for elliptic equations in domains with conical or angular points. Trudy Moskov. Mat. Obsc.16 (1967), 209–292 (in Russian); English translation in Trans. Moscow Math. Soc.16 (1967), 227–313

    Google Scholar 

  12. Kondrat'ev V.: Asymptotic of solution of the Navier-Stokes equations near the angular point of the boundary, J. Appl. Math. Mech.31 (1967), 125–129

    Google Scholar 

  13. Kozlov V.A., Maz'ya V.G.: On quasihomogeneous solutions to the Dirichlet problem for the Stokes system in a dihedral angle, Univ. Linköping LiTH-MAT-R-91-15 (preprint), 1991

  14. Kozlov V.A., Maz'ya V.G., Schwab C.: On singularities of solutions to the Dirichlet problem of hydrodynamics near the vertex of a 3-D cone, Univ. Linköping LiTH-MAT-R-90-23 (preprint) (1990)

  15. Kozlov V.A., Maz'ya V.G., Schwab C.: On singularities of solutions to the boundary value problems near the vertex of a rotational cone, Univ. Linköping LiTH-MAT-R-91-24 (preprint) (1991)

  16. Matsumura A., Nishida T.: Exterior stationary problems for the equations of motion of compressible viscous and heat conductive fluids. Proc. EQUADIFF 89. Ed. Dafermos, Ladas, Papanicolau, M. Dekker Inc. (1989), 473–479

    Google Scholar 

  17. Maz'ya V.G., Plamenevskii B.A.: About asymptotics of solutions of Navier-Stokes equations near edges, Dokl. Acad. Nauk SSSR210(4) (1973), 803–806

    Google Scholar 

  18. Maz'ya V.G., Plamenevskii B.A.: Problem of the motion of the fluid with a free surface in a vessel with edges, Problemy Mat. Analiza7, LGU (1979), 100–145 (in Russian)

    Google Scholar 

  19. Maz'ya V.G., Plamenevskii B.A.: On properties of solutions of threedimensional problems in the elasticity and hydrodynamics in domains with isolated singular points, Din. Sploschnoj Sredy50, Novosibirsk (1981), 99–121 (in Russian); English translation in Amer. Math. Soc. Transl.123 (1984), 109–123

    Google Scholar 

  20. Maz'ya V.G., Plamenevskii B.A.: First boundary value problem for the equations of hydrodynamics, Zap. Nauchn. Sem. LOMI96 (1980), 179–196 (in Russian); English translation in J. Sov. Math.21(5) (1983), 777–783

    Google Scholar 

  21. Maz'ya V.G., Plamenevskii B.A.: On the coefficients in the asymptotics of solutions of elliptic boundary value problems in domains with conical points, Math. Nachr.76 (1977), 29–60 (in Russian); English translation in Amer. Math. Soc. Transl.123(2) (1984), 57–88

    Google Scholar 

  22. Maz'ya V.G., Plamenevskii B.A.: Estimates inL p and Hölder classes and the Miranda-Agmon maximum principle for solutions of elliptic boundary value problems. Math. Nachr.81 (1978), 25–82 (in Russian); English translation in Amer. Math. Soc. Transl.123(2) (1984), 1–56

    Google Scholar 

  23. Maz'ya V.G., Plamenevskii B.A., Stupelis L.I.: The three-dimensional problem about the motion of fluid with the free boundary, Differential equations and their application, Vilnius,23 (1979), 29–153 (in Russian); English translation in Amer. Math. Soc. Transl.123(2) (1984), 171–268

    Google Scholar 

  24. Mizohata S.: The theory of partial differential equations, Cambridge Univ. Press (1973)

  25. Nazarov S.A., Plamenevskii B.A.: Elliptic boundary value problems in domains with picewise smooth boundary, Valter de Gruyter and Co, Berlin (1993)

    Google Scholar 

  26. Novotný A.: Steady flows of viscous compressible fluids in exterior domains under small perturbations of great potential forces, Math. Meth. Model. Appl. Sci.3(6),(1993), 725–757

    Google Scholar 

  27. Novotný A.: steady flows of viscous compressible fluids.L 2 approach, Proc. of EQUAM 92, Salvi R., Straskraba I., Eds. Math. Meth. Model. Appl. Sci. (in press)

  28. Novotný A.: On the steady transport equation. I.L p approach in domains with sufficiently smooth boundary Comm. Math. Univ. Carolinae (in press)

  29. Novotný A., Padula M.:L p-approach to steady flows of viscous compressible fluids in exterior domains, Arch. Rat. Mech. Anal.126 (1994), 243–297

    Google Scholar 

  30. Novotný A., Padula M.: Existence and uniqueness of stationary solutions for viscous compressible heat conductive fluid with large potential and small nonpotential external forces, Sib. Math. J.34(5) (1993), 120–146

    Google Scholar 

  31. Novotný A., Penel P.: OnL p-approach for steady flows of viscous compressible heat conductive gas. Math. Meth. Model. Appl. Sci. (in press)

  32. Osborn V.E.: Regularity of solutions of the Stokes problem in a polygonal domain, Num. Sol. of Part. Diff. Eq. III. Synspade 1975, Academic Press (1976), 393–421

  33. Padula M.: A representation formula for steady solutions of a compressible m fluid moving at low speed, Transp. Th. Stat. Phys.21 (1992), 593–614

    Google Scholar 

  34. Padula M.: Existence and uniqueness for viscous steady compressible motions, Arch. Rat. Mech. Anal.77(2) (1987), 89–102

    Google Scholar 

  35. Padula M.: Existence and uniqueness for viscous steady compressible motions, Proc. Sem. Fis. Mat. Trieste, Dinamica dei fluidi e dei gaz ionizzati (1982)

  36. Pileckas K., Zajaczkowski W.: On the free boundary problem for stationary compressible Navier-Stokes equations, Comm. Math. Phys.129 (1990), 169–204

    Google Scholar 

  37. Solonnikov V.A.: Solvability of the problem of plane motion of a heavy viscous incompressible capillary liquid, partially filling a container, Izv. Akad. Nauk SSSR43 (1977), 203–236 (in Russian); English translation in Math. USSR-Izv.14 (1980), 193–221

    Google Scholar 

  38. Solonnikov V.A.: On a free boundary problem for the system of Navier-Stokes equations, Trudy Sem. S.L. Sobolev2 (1978), 127–140 (in Russian)

    Google Scholar 

  39. Solonnikov V.A.: On the Stokes equation in domains with nonsmooth boundaries and on a viscous incompressible flow with a free surface, Nonlinear Part. Diff. Equations.3, College de France Seminar (1980/1981), 340–423

    Google Scholar 

  40. Solonnikov V.A.: Solvability of the three-dimensional boundary value problem with a free surface for the stationary Navier-Stokes system, Zap. Nauchn. Sem. LOMI84 (1976), 252–285 (in Russian); English translation in J. Sov. Math.21 (3) (1983), 427–450

    Google Scholar 

  41. Solonnikov V.A.: Solvability of three-dimensional boundary value problem with a free surface for the stationary Navier-Stokes system, Partial Differential Equations. Banach Center Publ.10 (1983), 361–403

    Google Scholar 

  42. Solonnikov V.A., Zajaczkowski W.: Neumann problem for second order elliptic equations in domains with edges on the boundary, Zap. Nauchn. Sem. LOMI127 (1983), 7–48 (in Russian); English translation in J. Sov. Math.27 (2) (1984), 2561–2586

    Google Scholar 

  43. Valli A.: On the existence of stationary solutions to compressible Navier-Stokes equations, Ann. Inst. H. Poincare,4(1) (1987), 99–113

    Google Scholar 

  44. Valli A.: Periodic and stationary solutions for compressible Navier-Stokes equations via stability method, Ann. Sc. Norm. Sup. Pisa4 (1983), 607–647

    Google Scholar 

  45. Zeidler E.: Vorlesungen über nichtlinearè functional Analysis I (Fixpunktsäte), Leipzig, (1976)

Download references

Author information

Authors and Affiliations

Authors

Additional information

Dedicated to Professor V.A. Solonnikov on his 60th birthday

Rights and permissions

Reprints and permissions

About this article

Cite this article

Nazarov, S.A., Novotný, A. & Pileckas, K. On steady compressible Navier-Stokes equations in plane domains with corners. Math. Ann. 304, 121–150 (1996). https://doi.org/10.1007/BF01446288

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01446288

Mathematics Subject Classifications (1991)

Navigation