Global Existence of Weak Solutions for the Anisotropic Compressible Stokes System

D. Bresch (1, 2) , Cosmin Burtea (3, 4)

1 LAMA - Laboratoire de Mathématiques
2 CNRS - Centre National de la Recherche Scientifique
3 UPD7 - Université Paris Diderot - Paris 7
4 IMJ-PRG (UMR_7586) - Institut de Mathématiques de Jussieu - Paris Rive Gauche

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 à 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.

Mots clés: Compressible Quasi-Stationary Stokes Equations; Anisotropic Viscous Tensor; Global Weak Solutions MSC: 35Q35; 35B25; 76T20

Domaines: Equations aux dérivées partielles [math.AP]

D. Bresch, Cosmin Burtea. Global Existence of Weak Solutions for the Anisotropic Compressible Stokes System. 2019. ⟨hal-02189797v1⟩