Asymptotic stability of stationary solutions to the compressible Euler-Maxwell equations Qingqing LiuChangjiang Zhu 35Q3535P20Compressible Euler-Maxwell equationsstationary solutionsasymptotic stability 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 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. Indiana University Mathematics Journal 2013 text pdf 10.1512/iumj.2013.62.5047 10.1512/iumj.2013.62.5047 en Indiana Univ. Math. J. 62 (2013) 1203 - 1235 state-of-the-art mathematics http://iumj.org/access/