Asymptotic Stability of the Stationary Solution to the Compressible Navier-Stokes Equations in the Half Space

Shuichi Kawashima, Shinya Nishibata, Peicheng Zhu

Research output: Contribution to journalArticle

71 Citations (Scopus)

Abstract

We investigate the existence and the asymptotic stability of a stationary solution to the initial boundary value problem for the compressible Navier-Stokes equation in a half space. The main concern is to analyze the phenomena that happens when the fluid blows out through the boundary. Thus, it is natural to consider the problem in the Eulerian coordinate. We have obtained the two results for this problem. The first result is concerning the existence of the stationary solution. We present the necessary and sufficient condition which ensures the existence of the stationary solution. Then it is shown that the stationary solution is time asymptotically stable if an initial perturbation is small in the suitable Sobolev space. The second result is proved by using an L2-energy method with the aid of the Poincaré type inequality.

Original languageEnglish
Pages (from-to)483-500
Number of pages18
JournalCommunications in Mathematical Physics
Volume240
Issue number3
DOIs
Publication statusPublished - 2003 Jan 1
Externally publishedYes

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Compressible Navier-Stokes Equations
half spaces
Stationary Solutions
Asymptotic Stability
Half-space
Navier-Stokes equation
Sobolev space
energy methods
boundary value problems
Energy Method
Asymptotically Stable
Initial-boundary-value Problem
Sobolev Spaces
perturbation
fluids
Perturbation
Necessary Conditions
Fluid
Sufficient Conditions

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

Cite this

Asymptotic Stability of the Stationary Solution to the Compressible Navier-Stokes Equations in the Half Space. / Kawashima, Shuichi; Nishibata, Shinya; Zhu, Peicheng.

In: Communications in Mathematical Physics, Vol. 240, No. 3, 01.01.2003, p. 483-500.

Research output: Contribution to journalArticle

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