Global existence of weak solutions for compressible Navier--Stokes equations: Thermodynamically unstable pressure and anisotropic viscous stress tensor
Global existence of weak solutions for compressible Navier--Stokes equations: Thermodynamically unstable pressure and anisotropic viscous stress tensor
复制标题
DOI：
10.4007/annals.2018.188.2.4
复制
发表时间：
2015-07
影响因子：
4.9
通讯作者：
D. Bresch;P. Jabin
中科院分区：
文献类型：
--
作者：
D. Bresch;P. Jabin
本文证明了可压缩Navier-Stokes方程在比P. L. Lions和E. Feireisl的理论更确切地说，我们专注于更一般的压力法律，这是不稳定的，我们也能够处理一些各向异性的粘性应力张量。为了回答这两个长期存在的问题，我们通过获得精确的定量正则性估计来重新审视经典的密度紧性理论：这需要对方程的结构进行更精确的分析，并结合一种新的方法来研究连续性方程的紧性。这两种情况使该理论有了重要的物理应用，例如描述太阳事件（维里压力定律）、地球物理流动（涡流粘度）或生物情况（各向异性）。
We prove global existence of appropriate weak solutions for the compressible Navier--Stokes 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).