Asymptotic behavior of solutions to the compressible Navier-Stokes equation in a cylindrical domain

Yoshiyuki Kagei, Takumi Nukumizu

Research output: Contribution to journalArticle

11 Citations (Scopus)

Abstract

Asymptotic behavior of solutions to the compressible Navier-Stokes equation around a given constant state is investigated on a cylindrical domain in R 3, under the no slip boundary condition for the velocity field. The L2 decay estimate is established for the perturbation from the constant state. It is also shown that the time-asymptotic leading part of the perturbation is given by a function satisfying a 1 dimensional heat equation. The proof is based on an energy method and asymptotic analysis for the associated linearized semigroup.

Original languageEnglish
Pages (from-to)987-1026
Number of pages40
JournalOsaka Journal of Mathematics
Volume45
Issue number4
Publication statusPublished - Dec 2008

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Compressible Navier-Stokes Equations
Asymptotic Behavior of Solutions
Perturbation
Slip Boundary Condition
Decay Estimates
Energy Method
Asymptotic Analysis
Heat Equation
Velocity Field
Semigroup

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Cite this

Asymptotic behavior of solutions to the compressible Navier-Stokes equation in a cylindrical domain. / Kagei, Yoshiyuki; Nukumizu, Takumi.

In: Osaka Journal of Mathematics, Vol. 45, No. 4, 12.2008, p. 987-1026.

Research output: Contribution to journalArticle

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