On the Navier–Stokes equations for three-dimensional compressible barotropic flow subject to large external potential forces with discontinuous initial data

Abstract

This paper concerns global weak solutions of the Navier–Stokes equations for three-dimensional compressible barotropic flow in the whole space R 3 subject to large external potential forces with discontinuous initial data. For general monotone increasing pressure, which includes the typical polytropic model for any positive ratio of specific heats, when there exists a unique steady state away from vacuum and the initial perturbation is suitably small in L 2 ∩ L ∞ for density and in H 1 for velocity, the authors obtain the global existence of weak solutions by making a full use of the structure of the compressible Navier–Stokes equations and the steady states.