Behaviour of weak solutions of compressible Navier-Stokes equations for isothermal fluids with a nonlinear stress tensor

Abstract

The aim of this paper is to study the behaviour of a weak solution to Navier-Stokes equations for isothermal fluids with a nonlinear stress tensor for time going to infinity. In an analogous way as in [18], we construct a suitable function which approximates the density for time going to infinity. Using properties of this function, we can prove the strong convergence of the density to its limit state. The behaviour of the velocity field and kinetic energy is mentioned as well.

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Correspondence to Rostislav Vodák.

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Vodák, R. Behaviour of weak solutions of compressible Navier-Stokes equations for isothermal fluids with a nonlinear stress tensor. J.evol.equ. 4, 213–247 (2004). https://doi.org/10.1007/s00028-003-0139-2

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Mathematics Subject Classification (2000):

  • 35Q30
  • 35B35
  • 76N10

Key words:

  • Stabilization
  • asymptotic behaviour
  • Navier-Stokes equations
  • isothermal fluids