# Global Existence of Weak Solutions for the Anisotropic Compressible Stokes System

## TL;DR

This paper proves the global existence of weak solutions for the anisotropic compressible Stokes system, overcoming previous limitations by controlling a defect measure related to pressure without restrictions on anisotropy.

## Contribution

It introduces a novel approach controlling a defect measure to establish global weak solutions without anisotropy restrictions.

## Key findings

- Established global existence of weak solutions for anisotropic compressible Stokes system.
- Developed a new method controlling a defect measure associated with pressure.
- Applicable to various fields like biology, porous media, and superconductivity.

## 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.