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In this paper, we study the problem of global existence of weak solutions forthe quasi-stationary compressible Stokes equations with an anisotropic viscoustensor. The key element of our proof is the control of a particular defectmeasure associated to the pressure which avoids the use of the eective ux.Using this new tool, we solve an open problem namely global existence ofsolutions {\`a} la Leray for such a system without assuming any restriction onthe anisotropy amplitude. It provides a exible and natural way to treatcompressible quasilinear Stokes systems which are important for instance inbiology, porous media, supra-conductivity or other applications in the lowReynolds number regime.

Global Existence of Weak Solutions for the Anisotropic Compressible Stokes System