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

Shuichi Kawashima, Peicheng Zhu

研究成果: ジャーナルへの寄稿学術誌査読

25 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.

本文言語英語
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
出版ステータス出版済み - 8月 2009

!!!All Science Journal Classification (ASJC) codes

  • 分析
  • 数学(その他)
  • 機械工学

フィンガープリント

「Asymptotic stability of rarefaction wave for the navier-stokes equations for a compressible fluid in the half space」の研究トピックを掘り下げます。これらがまとまってユニークなフィンガープリントを構成します。

引用スタイル