Compressible Navier--Stokes System with General Inflow-Outflow Boundary Data

Abstract

We prove existence of weak solutions to the compressible Navier--Stokes equations in a barotropic regime (adiabatic coefficient $\gamma>3/2$ in three dimensions, $\gamma>1$ 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 on either the shape of the inflow/outflow boundaries or the shape of the domain. The result applies also to pressure laws that are nonmonotone on a compact portion of the interval $[0,\infty)$.