On weak-strong uniqueness for compressible Navier-Stokes system with general pressure laws

Abstract: The goal of the present paper is to study the weak--strong uniqueness problem for the compressible Navier--Stokes system with a general barotropic pressure law. Our results include the case of a hard sphere pressure of Van der Waals type with a non--monotone perturbation and a Lipschitz perturbation of a monotone pressure. Although the main tool is the relative energy inequality, the results are conditioned by the presence of viscosity and do not seem extendable to the Euler system.