On the isentropic compressible Navier-Stokes equation

2005/11/08 by Antoine Mellet, Alexis F. Vasseur, Mellet, Antoine +1
Mathematics · Physics and Astronomy · #35D05 #35Q30 #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #math-ph #math.AP #math.MP #msc:35D05 #msc:35Q30

paper · pdf · doi:10.48550/arxiv.math/0511210

arxiv created 2005/11/08 · arxiv updated 2009/12/01

Abstract

We consider the compressible Navier-Stokes equation with density dependent viscosity coefficients, focusing on the case where those coefficients vanish on vacuum. We prove the stability of weak solutions both in the torus and in the whole space in dimension 2 and 3. The pressure is given by p=rho^gamma, and our result holds for any gamma>1. In particular, we obtain the stability of weak solutions of the Saint-Venant model for shallow water.

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