Stability of planar stationary solutions to the compressible Navier-Stokes equation on the half space

Yoshiyuki Kagei, Shuichi Kawashima

Research output: Contribution to journalArticle

45 Citations (Scopus)

Abstract

Stability of planar stationary solutions to the compressible Navier-Stokes equation on the half space ℝ+n (n ≥ 2)$$ under outflow boundary condition is investigated. It is shown that the planar stationary solution is stable with respect to small perturbations in Hs (ℝ+n) s ≥ [n/2]+1 and the perturbations decay in L norm as t →∞, provided that the magnitude of the stationary solution is sufficiently small. The stability result is proved by the energy method. In the proof an energy functional based on the total energy of the system plays an important role.

Original languageEnglish
Pages (from-to)401-430
Number of pages30
JournalCommunications in Mathematical Physics
Volume266
Issue number2
DOIs
Publication statusPublished - 2006 Sep 1
Externally publishedYes

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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