On the Long-time Behaviour of Solutions to the Navier-Stokes Equations of Compressible Flow

  • Eduard Feireisl
Part of the Progress in Nonlinear Differential Equations and Their Applications book series (PNLDE, volume 43)


Let be aspatialdomain filled with a fluid. We shall assume that the motion of the fluid is characterized by the velocity of the particle moving through attime. Moreover, for each timet,we shall suppose the fluid has a well-defined massdensity.


Weak Solution Compressible Flow Energy Inequality Oxford Science Publication Compressible Viscous Fluid 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    S.N. Antontsev, A.V. Kazhikhov and V.N. MonachovKrajevyje zadaci mechaniki neodnorodnych zidkostejNovosibirsk, 1983.Google Scholar
  2. [2]
    R. Coifman, P.L. Lions, Y. Meyer and S. Semmes, Compensated compactness and Hardy spacesJ. Math. Pures Appl. 72(1993), 247–286.MathSciNetMATHGoogle Scholar
  3. [3]
    R. Coifman and Y. Meyer, On commutators of singular integrals and bilinear singular integralsTrans. Amer. Math. Soc.212 (1975), 315–331.MathSciNetMATHCrossRefGoogle Scholar
  4. [4]
    R.J. DiPerna and P.L. Lions, Ordinary differential equations, transport theory and Sobolev spacesInvent. Math.98 (1989), 511–547.MathSciNetMATHCrossRefGoogle Scholar
  5. [5]
    E. Feireisl, Š. Matušů-Nečasová, H. Petzeltová and I. Straškraba, On the motion of a viscous compressible flow driven by a time-periodic external flowArch. Rational Mech. Anal. 149(1999), 69–96.MATHCrossRefGoogle Scholar
  6. [6]
    E. Feireisl, A. Novotný and H. Petzeltová, On the existence of globally defined weak solutions to the Navier-Stokes equations of isentropic compressible fluidsJ. Math. Fluid Mech.2000, submitted.Google Scholar
  7. [7]
    E. Feireisl and H. Petzeltová, On the long time behaviour of solutions to the Navier-Stokes equations of compressible flowArch. Rational Mech. Anal. 150(1999), 77–96.MATHCrossRefGoogle Scholar
  8. [8]
    E. Feireisl and H. Petzeltová, On compactness of solutions to the Navier-Stokes equations of compressible flowJ. Differential Equations163 (2000), 57–75.MathSciNetMATHCrossRefGoogle Scholar
  9. [9]
    E. Feireisl and H. Petzeltová, On the steady state solutions to the Navier-Stokes equations of compressible flowManuscripta Math. 97(1998), 109–116.MathSciNetMATHCrossRefGoogle Scholar
  10. [10]
    G.P. GaldiAn Introduction to the Mathematical Theory of the NavierStokes Equations ISpringer-Verlag, New York, 1994.Google Scholar
  11. [11]
    D. Hoff, Spherically symmetric solutions of the Navier-Stokes equations for compressible, isothermal flow with large, discontinuous initial dataIndiana Univ. Math. J.41 (1992), 1225–1302.MathSciNetMATHCrossRefGoogle Scholar
  12. [12]
    D. Hoff, Strong convergence to global solutions for multidimensional flows of compressible, viscous fluids with polytropic equations of state and discontinuous initial dataArch. Rational Mech. Anal. 132 (1995), 1–14.MathSciNetMATHCrossRefGoogle Scholar
  13. [13]
    O.A. LadyzhenskayaThe Mathematical Theory of Viscous Incompressible FlowGordon and Breach, New York, 1969.MATHGoogle Scholar
  14. [14]
    P.L. LionsMathematical Topics in Fluid Dynamics Vol. 1 Incompressible Models Oxford Science Publication, Oxford, 1996.Google Scholar
  15. [15]
    P.L. LionsMathematical Topics in Fluid Dynamics Vol. 2 Compressible Models Oxford Science Publication, Oxford, 1998.Google Scholar
  16. [16]
    A. Matsumura and T. Nishida, The initial value problem for the equations of motion of compressible and heat conductive fluidsComm. Math. Phys. 89 (1983), 445–464.MathSciNetMATHCrossRefGoogle Scholar
  17. [17]
    D. Serre, Solutions faibles globales des équations de Navier-Stokes pour un fluide compressibleC. R. Acad. Sci.Paris 303 (1986), 639–642.MATHGoogle Scholar
  18. [18]
    I. Straškraba, Asymptotic development of vacuum of 1-dimensional Navier-Stokes equations of compressible flowNonlinear World3 (1996), 519–533.MathSciNetMATHGoogle Scholar
  19. [19]
    R. TemamNavier-Stokes EquationsNorth-Holland, Amsterdam, 1977.MATHGoogle Scholar
  20. [20]
    V.A. Vaigant and A.V. Kazhikhov, On the existence of global solutions to two-dimensional Navier-Stokes equations of a compressible viscous fluidSibirskij Math. Z.36 (1995), 1283–1316. (In Russian).MathSciNetGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2001

Authors and Affiliations

  • Eduard Feireisl
    • 1
  1. 1.Institute of Mathematics AV ČRCzech Republic

Personalised recommendations