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

Fingerprint

Euler System
Maxwell System
Stationary Solutions
Asymptotic Convergence
Energy Method
A Priori Estimates
Global Solution
Asymptotic Stability
Existence and Uniqueness
Regularity
Infinity
Decay
Tend
Verify
Perturbation

Keywords

  • asymptotic stability
  • regularity-loss
  • stationary solution

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Stability of stationary solutions for the non-isentropic Euler-Maxwell system in the whole space. / Ueda, Yoshihiro; Kawashima, Shuichi.

In: Bulletin of the Brazilian Mathematical Society, Vol. 47, No. 2, 01.06.2016, p. 787-797.

Research output: Contribution to journalArticle

@article{2ef10e7cd1684fb0bfec34192217b8c6,
title = "Stability of stationary solutions for the non-isentropic Euler-Maxwell system in the whole space",
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.",
keywords = "asymptotic stability, regularity-loss, stationary solution",
author = "Yoshihiro Ueda and Shuichi Kawashima",
year = "2016",
month = "6",
day = "1",
doi = "10.1007/s00574-016-0186-2",
language = "English",
volume = "47",
pages = "787--797",
journal = "Bulletin of the Brazilian Mathematical Society",
issn = "1678-7544",
publisher = "Springer New York",
number = "2",

}

TY - JOUR

T1 - Stability of stationary solutions for the non-isentropic Euler-Maxwell system in the whole space

AU - Ueda, Yoshihiro

AU - Kawashima, Shuichi

PY - 2016/6/1

Y1 - 2016/6/1

N2 - 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.

AB - 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.

KW - asymptotic stability

KW - regularity-loss

KW - stationary solution

UR - http://www.scopus.com/inward/record.url?scp=84976384134&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84976384134&partnerID=8YFLogxK

U2 - 10.1007/s00574-016-0186-2

DO - 10.1007/s00574-016-0186-2

M3 - Article

VL - 47

SP - 787

EP - 797

JO - Bulletin of the Brazilian Mathematical Society

JF - Bulletin of the Brazilian Mathematical Society

SN - 1678-7544

IS - 2

ER -