Global Existence of Weak Solutions for the Anisotropic Compressible Stokes System
Abstract
In this paper, we study the problem of global existence of weak solutions for the quasi-stationary compressible Stokes equations with an anisotropic viscous tensor. The key element of our proof is the control of a particular defect measure associated to the pressure which avoids the use of the eective ux. Using this new tool, we solve an open problem namely global existence of solutions {\`a} la Leray for such a system without assuming any restriction on the anisotropy amplitude. It provides a exible and natural way to treat compressible quasilinear Stokes systems which are important for instance in biology, porous media, supra-conductivity or other applications in the low Reynolds number regime.
Keywords
Cite
@article{arxiv.1907.09171,
title = {Global Existence of Weak Solutions for the Anisotropic Compressible Stokes System},
author = {Didier Bresch and Cosmin Burtea},
journal= {arXiv preprint arXiv:1907.09171},
year = {2022}
}
Comments
Compared to the version in Ann. IHP. : Revised argument in the proof of Theorem 2.10, main results unchanged : the proof of the main result was incomplete because we cannot prove that the defect measure vanishes at initial time. We prove instead that the mean value of the defect measure over any interval [0,T] is 0. This is sufficient in order to identify the pressure. See Lemmas 2.11 and 2.12