Title: Asymptotic stability of stationary solutions to the compressible Euler-Maxwell equations

Authors: Qingqing Liu and Changjiang Zhu

Issue: Volume 62 (2013), Issue 4, 1203-1235


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.