Contraction property for large perturbations of shocks of the barotropic Navier–Stokes system

Abstract

This paper is dedicated to the construction of a pseudo-norm for which small shockprofiles of the barotropic Navier–Stokes equations have a contraction property. This contraction property holds in the class of any large solutions to the barotropic Navier–Stokes equations. It implies a stability condition which is independent of the strength of the viscosity. The proof is based on the relative entropy method, and is related to the notion of $a$-contraction first introduced by the authors in the hyperbolic case.