Global existence of weak solutions for compressible Navier-Stokese quations: Thermodynamically unstable pressure and anisotropic viscous stress tensor

Didier Bresch, Pierre Emmanuel Jabin

Research output: Contribution to journalArticlepeer-review

34 Scopus citations

Abstract

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).

Original languageEnglish (US)
Pages (from-to)577-684
Number of pages108
JournalAnnals of Mathematics
Volume188
Issue number2
DOIs
StatePublished - 2018

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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