  In this paper, we are concerned with the compressible Euler-Maxwell equations
with a 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 first show the asymptotic
stability of solutions to the Cauchy problem near the stationary state provided
that the initial perturbation is sufficiently small. Moreover the convergence
rates are obtained by combining the $L^p$-$L^q$ estimates for the linearized
equations with time-weighted estimate.
