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 journalArticlepeer-review

    83 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 2002

    All Science Journal Classification (ASJC) codes

    • Analysis
    • Mathematics (miscellaneous)
    • Mechanical Engineering

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