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 , 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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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
Mathematics Subject Classification (2000):
- asymptotic behaviour
- Navier-Stokes equations
- isothermal fluids