On the rate of decay of the oseen semigroup in exterior domains and its application to Navier-Stokes equation

Yuko Enomoto, Yoshihiro Shibata

    Research output: Contribution to journalArticle

    32 Citations (Scopus)

    Abstract

    We prove L p -L q estimates of the Oseen semigroup in n-dimensional exterior domains $$(n\,\geqslant\, 3),$$ which refine and improve those obtained by Kobayashi and Shibata [15]. As an application, we give a globally in time stability theory for the stationary Navier-Stokes flow whose velocity at infinity is a non-zero constant vector. We thus extend the result of Shibata [21]. In particular, we find an optimal rate of convergence of solutions of the non-stationary problem to those of the corresponding stationary problem.

    Original languageEnglish
    Pages (from-to)339-367
    Number of pages29
    JournalJournal of Mathematical Fluid Mechanics
    Volume7
    Issue number3
    DOIs
    Publication statusPublished - 2005 Aug

    Fingerprint

    Stokes flow
    Exterior Domain
    Navier-Stokes equations
    Flow velocity
    Navier-Stokes equation
    flow velocity
    infinity
    Navier Stokes equations
    Navier-Stokes Equations
    Semigroup
    Decay
    Convergence of Solutions
    Optimal Rate of Convergence
    Stokes Flow
    Stability Theory
    decay
    estimates
    Navier-Stokes
    n-dimensional
    Infinity

    Keywords

    • Exterior domain
    • L -L estimate
    • Oseen semigroup
    • Stability
    • Stationary solution

    ASJC Scopus subject areas

    • Materials Science (miscellaneous)
    • Oceanography
    • Fluid Flow and Transfer Processes
    • Applied Mathematics

    Cite this

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    AU - Shibata, Yoshihiro

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    AB - We prove L p -L q estimates of the Oseen semigroup in n-dimensional exterior domains $$(n\,\geqslant\, 3),$$ which refine and improve those obtained by Kobayashi and Shibata [15]. As an application, we give a globally in time stability theory for the stationary Navier-Stokes flow whose velocity at infinity is a non-zero constant vector. We thus extend the result of Shibata [21]. In particular, we find an optimal rate of convergence of solutions of the non-stationary problem to those of the corresponding stationary problem.

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    KW - L -L estimate

    KW - Oseen semigroup

    KW - Stability

    KW - Stationary solution

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