Global Existence of Weak Solutions for Compresssible NavierStokes Equations: Thermodynamically unstable pressure and anisotropic viscous stress tensor
Abstract
We prove global existence of appropriate weak solutions for the compressible NavierStokes equations for more general stress tensor than those covered by P.L. Lions and E. Feireisl's theory. More precisely we focus on more general pressure laws which are not thermodynamically stable; we are also able to handle some anisotropy in the viscous stress tensor. To give answers to these two longstanding problems, we revisit the classical compactness theory on the density by obtaining precise quantitative regularity estimates: This requires a more precise analysis of the structure of the equations combined to a novel approach to the compactness of the continuity equation. These two cases open the theory to important physical applications, for instance to describe solar events (virial pressure law), geophysical flows (eddy viscosity) or biological situations (anisotropy).
 Publication:

arXiv eprints
 Pub Date:
 July 2015
 DOI:
 10.48550/arXiv.1507.04629
 arXiv:
 arXiv:1507.04629
 Bibcode:
 2015arXiv150704629B
 Keywords:

 Mathematics  Analysis of PDEs;
 Mathematical Physics;
 Physics  Fluid Dynamics;
 35Q30;
 35D30;
 54D30;
 42B37;
 35Q86;
 92B05