We prove global existence of appropriate weak solutions for the com- pressible Navier-Stokese quations for amoregeneral stress tensor than those previously covered by P.-L. Lionsand E. Feireisl's theory. Morepre- cisely we focus on more general pressure laws that are not thermodynami- callystable; 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).
All Science Journal Classification (ASJC) codes
- Statistics and Probability
- Statistics, Probability and Uncertainty