On a resolvent estimate of the Stokes system in a half space arising from a free boundary problem for the Navier-Stokes equations

Yoshihiro Shibata, S. Shimizu

    Research output: Contribution to journalArticle

    6 Citations (Scopus)

    Abstract

    In this paper we consider a resolvent problem of the Stokes operator with some boundary condition in the half space, which is obtained as a model problem arising in evolution free boundary problems for viscous, incompressible fiuidfiow. We show standard resolvent estimates in the Lq framework (1 <q< ∞), applying some kernel estimates to concrete solution formulas. The Volevich trick in [21] plays a fundamental role in estimating solutions.

    Original languageEnglish
    Pages (from-to)482-499
    Number of pages18
    JournalMathematische Nachrichten
    Volume282
    Issue number3
    DOIs
    Publication statusPublished - 2009 Mar

    Fingerprint

    Resolvent Estimates
    Stokes System
    Free Boundary Problem
    Half-space
    Navier-Stokes Equations
    Stokes Operator
    Kernel Estimate
    Resolvent
    Boundary conditions
    Model
    Standards
    Framework

    Keywords

    • Free boundary problem
    • Gravity force
    • L framework
    • Resolvent estimate
    • Stokes equation
    • Surface tension

    ASJC Scopus subject areas

    • Mathematics(all)

    Cite this

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    AU - Shimizu, S.

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    KW - Stokes equation

    KW - Surface tension

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