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 - Sep 1 2006

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Compressible Navier-Stokes Equations
half spaces
Stationary Solutions
Half-space
Navier-Stokes equation
perturbation
energy methods
norms
Energy Method
Energy Functional
boundary conditions
Small Perturbations
energy
decay
Decay
Perturbation
Norm
Boundary conditions
Energy

All Science Journal Classification (ASJC) codes

  • Physics and Astronomy(all)
  • Statistical and Nonlinear Physics
  • Mathematical Physics

Cite this

Stability of planar stationary solutions to the compressible Navier-Stokes equation on the half space. / Kagei, Yoshiyuki; Kawashima, Shuichi.

In: Communications in Mathematical Physics, Vol. 266, No. 2, 01.09.2006, p. 401-430.

Research output: Contribution to journalArticle

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