Stability of stationary solutions for the non-isentropic Euler-Maxwell system in the whole space

Yoshihiro Ueda, Shuichi Kawashima

Research output: Contribution to journalArticle

Abstract

In this paper we discuss the asymptotic stability of stationary solutions for the non-isentropic Euler-Maxwell system in R3. It is known in the authors’ previous works [17, 18, 19] that the Euler-Maxwell system verifies the decay property of the regularity-loss type. In this paper we first prove the existence and uniqueness of a small stationary solution. Then we show that the non-stationary problemhas a global solution in a neighborhood of the stationary solution under smallness condition on the initial perturbation. Moreover, we show the asymptotic convergence of the solution toward the stationary solution as time tends to infinity. The crucial point of the proof is to derive a priori estimates by using the energy method.

Original languageEnglish
Pages (from-to)787-797
Number of pages11
JournalBulletin of the Brazilian Mathematical Society
Volume47
Issue number2
DOIs
Publication statusPublished - 2016 Jun 1
Externally publishedYes

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Keywords

  • asymptotic stability
  • regularity-loss
  • stationary solution

ASJC Scopus subject areas

  • Mathematics(all)

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