On the maximal L p-L q regularity of the Stokes problem with first order boundary condition; model problems

Yoshihiro Shibata, Senjo Shimizu

    Research output: Contribution to journalArticle

    19 Citations (Scopus)

    Abstract

    In this paper, we proved the generalized resolvent estimate and the maximal L p-L q regularity of the Stokes equation with first order boundary condition in the half-space, which arises in the mathematical study of the motion of a viscous incompressible one phase fluid flow with free surface. The core of our approach is to prove the R boundedness of solution operators defined in a sector Σ ∈,γ0 = {λ ∈ C \ {0}

    Original languageEnglish
    Pages (from-to)561-626
    Number of pages66
    JournalJournal of the Mathematical Society of Japan
    Volume64
    Issue number2
    DOIs
    Publication statusPublished - 2012

    Fingerprint

    R-boundedness
    Resolvent Estimates
    Boundedness of Solutions
    Stokes Problem
    Stokes Equations
    Free Surface
    Half-space
    Fluid Flow
    Sector
    Regularity
    First-order
    Boundary conditions
    Motion
    Operator
    Model

    Keywords

    • Gravity force
    • Half space problem
    • Maximal regularity
    • Resolvent estimate
    • Stokes equation
    • Surface tension

    ASJC Scopus subject areas

    • Mathematics(all)

    Cite this

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    AU - Shimizu, Senjo

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    AB - In this paper, we proved the generalized resolvent estimate and the maximal L p-L q regularity of the Stokes equation with first order boundary condition in the half-space, which arises in the mathematical study of the motion of a viscous incompressible one phase fluid flow with free surface. The core of our approach is to prove the R boundedness of solution operators defined in a sector Σ ∈,γ0 = {λ ∈ C \ {0}

    KW - Gravity force

    KW - Half space problem

    KW - Maximal regularity

    KW - Resolvent estimate

    KW - Stokes equation

    KW - Surface tension

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