On a generalized resolvent estimate for the Stokes system with Robin boundary condition

Yoshihiro Shibata, Rieko Shimada

    Research output: Contribution to journalArticle

    35 Citations (Scopus)

    Abstract

    We prove a generalized resolvent estimate of Stokes equations with nonhomogeneous Robin boundary condition and divergence condition in the L q framework (1 < q < ∞) in a domain of Rn (n ≧ 2) that is a bounded domain or the exterior of a bounded domain. The Robin condition consists of two conditions: v · u = 0 and au + β(T(u, p)v -(T(u, p)u, v)v) = h on the boundary of the domain with α, β ≧ 0 and α + β= 1, where u denotes a velocity vector, p a pressure, T(u, p) the stress tensor for the Stokes flow, and v the unit outer normal to the boundary of the domain. It presents the slip condition when β=1 and the non-slip one when α = 1, respectively.

    Original languageEnglish
    Pages (from-to)469-519
    Number of pages51
    JournalJournal of the Mathematical Society of Japan
    Volume59
    Issue number2
    DOIs
    Publication statusPublished - 2007 Apr

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    Resolvent Estimates
    Stokes System
    Robin Boundary Conditions
    Bounded Domain
    Nonhomogeneous Boundary Conditions
    Slip Condition
    Stokes Equations
    Stokes Flow
    Stress Tensor
    Divergence
    Denote
    Unit

    Keywords

    • Resolvent estimate
    • Robin boundary condition
    • Stokes system

    ASJC Scopus subject areas

    • Mathematics(all)

    Cite this

    On a generalized resolvent estimate for the Stokes system with Robin boundary condition. / Shibata, Yoshihiro; Shimada, Rieko.

    In: Journal of the Mathematical Society of Japan, Vol. 59, No. 2, 04.2007, p. 469-519.

    Research output: Contribution to journalArticle

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