Weak Solutions for the Stationary Anisotropic and Nonlocal Compressible Navier-Stokes System

2020/03/10 by Bresch, D., Burtea, Cosmin · 1 citation
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2003.04587

Abstract

In this paper, we prove global existence of weak solutions for the stationary compressible Navier-Stokes equations with an anisotropic and nonlocal viscous term in a periodic domain. This gives an answer to an open problem important for applications in geophysics or in microuidics. The main idea is to adapt in a non-trivial way the new idea developped by the authors in a previous paper, see [2] which allowed them to treat the anisotropic compressible quasi-stationary Stokes system.

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• On dissipative turbulent solutions to the compressible anisotropic Navier-Stokes equations in unbounded domains

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