Lp-Lq estimate of the stokes operator and navier-stokes flows in the exterior of a rotating obstacle

Toshiaki Hishida, Yoshihiro Shibata

    Research output: Contribution to journalArticle

    42 Citations (Scopus)

    Abstract

    We consider the motion of a viscous fluid filling the whole three-dimensional space exterior to a rotating obstacle with constant angular velocity. We develop the L estimate and the similar estimates in the Lorentz spaces of the Stokes semigroup with rotation effect. We next apply them to the Navier-Stokes equation to prove the global existence of a unique solution which goes to a stationary flow as t → ∞ with some definite rates when both the stationary flow and the initial disturbance are sufficiently small in L (weak-L .

    Original languageEnglish
    Pages (from-to)339-421
    Number of pages83
    JournalArchive for Rational Mechanics and Analysis
    Volume193
    Issue number2
    DOIs
    Publication statusPublished - 2009 Aug

    Fingerprint

    Stokes Operator
    Lp Estimates
    Stokes Flow
    Angular velocity
    Navier-Stokes
    Navier Stokes equations
    Rotating
    Fluids
    Lorentz Spaces
    Stokes
    Viscous Fluid
    Unique Solution
    Estimate
    Global Existence
    Navier-Stokes Equations
    Semigroup
    Disturbance
    Three-dimensional
    Motion

    ASJC Scopus subject areas

    • Analysis
    • Mechanical Engineering
    • Mathematics (miscellaneous)

    Cite this

    Lp-Lq estimate of the stokes operator and navier-stokes flows in the exterior of a rotating obstacle. / Hishida, Toshiaki; Shibata, Yoshihiro.

    In: Archive for Rational Mechanics and Analysis, Vol. 193, No. 2, 08.2009, p. 339-421.

    Research output: Contribution to journalArticle

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