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

• 成果类型: Article
• 署名作者: Bresch, Didier; Jabin, Pierre-emmanuel
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2018.188.2.4
• 发表日期: 2018
• 页码: 577-684
• 关键词: finite volume scheme; differential-equations; renormalized solutions; transport-equations; cauchy-problem; vector-fields; mac scheme; part ii; bv; uniqueness

摘要

We prove global existence of appropriate weak solutions for the compressible Navier-Stokes equations for a more general stress tensor than those previously covered by P.-L.Lions and E. Feireisl's theory. More precisely we focus on more general pressure laws that 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).