On the compressible viscous barotropic flows subject to large external potential forces in a half space with Navier's boundary conditions

Abstract

This paper is concerned with an initial and boundary value problem of the Navier‐Stokes equations for compressible viscous barotropic flow subject to large external potential forces in a half space with Navier's boundary conditions. The global well‐posedness of strong solutions with large oscillations and vacuum is established, provided that the initial energy is suitably small and that the unique steady state is strictly away from vacuum. As a by‐product, the stability of stationary solution is obtained.