Asymptotic Stability Of The Compressible Navier-Stokes-Maxwell Equations

In this paper, we are concerned with the compressible Navier-Stokes-Maxwell equations with nonconstant background density (e.g. of ions) in three dimensional space. There exist stationary solutions when the background density is a small perturbation of a positive constant state. We prove the asymptotic stability of solutions to the Cauchy problem near the stationary state provided that the initial perturbation is sufficiently small.