Compressible Navier-Stokes system with general inflow-outflow boundary data

Abstract : We prove existence of weak solutions to the compressible Navier-Stokes equations in barotropic regime (adiabatic coefficient γ > 3/2, in three dimensions, γ > 1 in two dimensions) with large velocity prescribed at the boundary and large density prescribed at the inflow boundary of a bounded sufficiently smooth domain, without any restriction neither on the shape of the inflow/outflow boundaries nor on the shape of the domain. The result applies also to pressure laws that are non monotone on a compact portion of interval [0, ∞).