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

We prove existence of weak solutions to the compressible Navier--Stokes equations in a 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 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,∞).