On large-time behavior of solutions to the compressible Navier-Stokes equations in the half space in R3

Yoshiyuki Kagei, Takayuki Kobayashi

Research output: Contribution to journalArticle

58 Citations (Scopus)

Abstract

The Navier-Stokes equation for compressible viscous fluid is considered on the half space in R3 under the zero-Dirichlet boundary condition for the momentum with initial data near an arbitrarily given equilibrium of positive constant density and zero momentum. Time decay properties in L2 norms for solutions of the linearized problem are investigated to obtain the rate of convergence in L2 norms of solutions to the equilibrium when initial data are sufficiently close to the equilibrium in H3 ∩ L1. Some lower bounds are derived for solutions to the linearized problem, one of which indicates a nonlinear phenomenon not appearing in the case of the Cauchy problem on the whole space.

Original languageEnglish
Pages (from-to)89-159
Number of pages71
JournalArchive for Rational Mechanics and Analysis
Volume165
Issue number2
DOIs
Publication statusPublished - Nov 1 2002

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Compressible Navier-Stokes Equations
Large Time Behavior
Behavior of Solutions
Half-space
Navier Stokes equations
Momentum
Norm
Nonlinear Phenomena
Compressible Fluid
Zero
Viscous Fluid
Dirichlet Boundary Conditions
Cauchy Problem
Navier-Stokes Equations
Rate of Convergence
Boundary conditions
Decay
Lower bound
Fluids

All Science Journal Classification (ASJC) codes

  • Analysis
  • Mathematics (miscellaneous)
  • Mechanical Engineering

Cite this

On large-time behavior of solutions to the compressible Navier-Stokes equations in the half space in R3. / Kagei, Yoshiyuki; Kobayashi, Takayuki.

In: Archive for Rational Mechanics and Analysis, Vol. 165, No. 2, 01.11.2002, p. 89-159.

Research output: Contribution to journalArticle

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