Asymptotic stability of rarefaction wave for the navier-stokes equations for a compressible fluid in the half space

Shuichi Kawashima, Peicheng Zhu*

*この研究の対応する著者

研究成果: Article査読

27 被引用数 (Scopus)

抄録

This paper is concerned with the asymptotic stability towards a rarefaction wave of the solution to an outflow problem for the Navier-Stokes equations in a compressible fluid in the Eulerian coordinate in the half space. This is the second one of our series of papers on this subject. In this paper, firstly we classify completely the time-asymptotic states, according to some parameters, that is the spatial-asymptotic states and boundary conditions, for this initial boundary value problem, and some pictures for the classification of time-asymptotic states are drawn in the state space. In order to prove the stability of the rarefaction wave, we use the solution to Burgers' equation to construct a suitably smooth approximation of the rarefaction wave and establish some time-decay estimates in Lp-norm for the smoothed rarefaction wave. We then employ the L2-energy method to prove that the rarefaction wave is non-linearly stable under a small perturbation, as time goes to infinity.

本文言語English
ページ(範囲)105-132
ページ数28
ジャーナルArchive for Rational Mechanics and Analysis
194
1
DOI
出版ステータスPublished - 2009 8月
外部発表はい

ASJC Scopus subject areas

  • 分析
  • 数学(その他)
  • 機械工学

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