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

Toshiaki Hishida, Yoshihiro Shibata

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    43 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

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    ASJC Scopus subject areas

    • Analysis
    • Mechanical Engineering
    • Mathematics (miscellaneous)

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