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

2014/03/26 by Qingqing Liu, Changjiang Zhu · 1 citation
Mathematics · #math.AP

paper · pdf

published as Indiana University Mathematics Journal, Vol. 62, No. 4 (2013) · 25 pages. arXiv admin note: text overlap with arXiv:1006.3606 by other authors

arxiv created 2014/03/26 · arxiv updated 2014/03/27

Abstract

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.

Citations

• Global Smooth Flows for the Compressible Euler-Maxwell System: Relaxation Case

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