Skip to main content
Disciplines
Automotive Business IT + Informatics Construction + Real Estate Electrical Engineering + Electronics Energy + Sustainability Insurance + Risk Finance + Banking Management + Leadership Marketing + Sales Mechanical Engineering + Materials
Events
DE
EN
Books
Journals
Topic Page
Marketing
Start single access now
Access for companies
EXTENDED SEARCH
Log in
Top
Published in:
The Work of Yoshihiro Shibata Read chapter Read first chapter

2016 | OriginalPaper | Chapter

Stability of Time Periodic Solutions for the Rotating Navier-Stokes Equations

Authors : Tsukasa Iwabuchi, Alex Mahalov, Ryo Takada

Published in: Recent Developments of Mathematical Fluid Mechanics

Publisher: Springer Basel

Log in

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Abstract

We consider the stability problem of time periodic solutions for the rotating Navier-Stokes equations. For the non-rotating case, it is known that time periodic solutions to the original Navier-Stokes equations are asymptotically stable under the smallness assumptions both on the time periodic solutions and on the initial disturbances. We shall treat the high-rotating cases, and prove the asymptotic stability of large time periodic solutions for large initial perturbations.

Dont have a licence yet? Then find out more about our products and how to get one now:

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!

inform now

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!

inform now

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!

inform now
previous chapter On the Weak Solution of the Fluid-Structure Interaction Problem for Shear-Dependent Fluids
next chapter Weighted L p − L q Estimates of Stokes Semigroup in Half-Space and Its Application to the Navier-Stokes Equations
Literature
1.
A. Babin, A. Mahalov, B. Nicolaenko, Long-time averaged Euler and Navier-Stokes equations for rotating fluids, in Advanced Series in Nonlinear Dynamics, vol. 7 (World Scientific Publishing, River Edge, NJ, 1995), pp. 145–157MATH
2.
A. Babin, A. Mahalov, B. Nicolaenko, Regularity and integrability of 3D Euler and Navier-Stokes equations for rotating fluids. Asymptot. Anal. 15, 103–150 (1997)MathSciNetMATH
3.
A. Babin, A. Mahalov, B. Nicolaenko, Global regularity of 3D rotating Navier-Stokes equations for resonant domains. Indiana Univ. Math. J. 48, 1133–1176 (1999)MathSciNetMATH
4.
A. Babin, A. Mahalov, B. Nicolaenko, 3D Navier-Stokes and Euler equations with initial data characterized by uniformly large vorticity. Indiana Univ. Math. J. 50, 1–35 (2001)MathSciNetCrossRefMATH
5.
J.-Y. Chemin, B. Desjardins, I. Gallagher, E. Grenier, Anisotropy and dispersion in rotating fluids, in Nonlinear Partial Differential Equations and Their Applications. Collège de France Seminar, Paris, 1997/1998, vol. XIV. Studies in Mathematics and Its Applications, vol. 31, (North-Holland, Amsterdam, 2002), pp. 171–192
6.
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)
7.
F. Flandoli, A. Mahalov, Stochastic three-dimensional rotating Navier-Stokes equations: averaging, convergence and regularity. Arch. Ration. Mech. Anal. 205, 195–237 (2012)MathSciNetCrossRefMATH
8.
M. Hieber, Y. Shibata, The Fujita-Kato approach to the Navier-Stokes equations in the rotational framework. Math. Z. 265, 481–491 (2010)MathSciNetCrossRefMATH
9.
T. Iwabuchi, R. Takada, Time periodic solutions to the Navier-Stokes equations in the rotational framework. J. Evol. Equ. 12, 985–1000 (2012)MathSciNetCrossRefMATH
10.
T. Iwabuchi, R. Takada, Global solutions for the Navier-Stokes equations in the rotational framework. Math. Ann. 357, 727–741 (2013)MathSciNetCrossRefMATH
11.
T. Kato, Strong \(L^{p}\)-solutions of the Navier-Stokes equation in \(\boldsymbol{R}^{m}\), with applications to weak solutions, Math. Z. 187, 471–480 (1984)MathSciNetCrossRefMATH
12.
Y. Koh, S. Lee, R. Takada, Dispersive estimates for the Navier-Stokes equations in the rotational framework. Adv. Differ. Equ. 19, 857–878 (2014)MathSciNetMATH
13.
P. Konieczny, T. Yoneda, On dispersive effect of the Coriolis force for the stationary Navier-Stokes equations. J. Differ. Equ. 250, 3859–3873 (2011)MathSciNetCrossRefMATH
14.
H. Kozono, M. Nakao, Periodic solutions of the Navier-Stokes equations in unbounded domains. Tohoku Math. J. (2) 48, 33–50 (1996)
15.
16.
H. Kozono, Y. Mashiko, R. Takada, Existence of periodic solutions and their asymptotic stability to the Navier-Stokes equations with the Coriolis force. J. Evol. Equ. 14, 565–601 (2014)MathSciNetCrossRefMATH
17.
P. Maremonti, Existence and stability of time-periodic solutions to the Navier-Stokes equations in the whole space. Nonlinearity 4, 503–529 (1991)MathSciNetCrossRefMATH
18.
P. Maremonti, Some theorems of existence for solutions of the Navier-Stokes equations with slip boundary conditions in half-space. Ricerche mat. 40, 81–135 (1991)MathSciNetMATH
19.
Y. Taniuchi, On stability of periodic solutions of the Navier-Stokes equations in unbounded domains. Hokkaido Math. J. 28, 147–173 (1999)MathSciNetCrossRefMATH
20.
M. Yamazaki, The Navier-Stokes equations in the weak-\(L^{n}\) space with time-dependent external force. Math. Ann. 317, 635–675 (2000)MathSciNetCrossRefMATH
21.
M. Yamazaki, Solutions in the Morrey spaces of the Navier-Stokes equation with time-dependent external force. Funkcial. Ekvac. 43, 419–460 (2000)MathSciNetMATH
Metadata
Title
Stability of Time Periodic Solutions for the Rotating Navier-Stokes Equations
Authors
Tsukasa Iwabuchi
Alex Mahalov
Ryo Takada
Copyright Year
2016
Publisher
Springer Basel
Book
Recent Developments of Mathematical Fluid Mechanics

Print ISBN: 978-3-0348-0938-2

Electronic ISBN: 978-3-0348-0939-9

Copyright Year: 2016

DOI
https://doi.org/10.1007/978-3-0348-0939-9_17

Premium Partner

    Image Credits