L p-L q maximal regularity and viscous incompressible flows with free surface

Yoshihiro Shibata, Senjo Shimizu

    Research output: Contribution to journalArticle

    8 Citations (Scopus)

    Abstract

    We prove the L p-L q maximal regularity of solutions to the Neumann problem for the Stokes equations with non-homogeneous boundary condition and divergence condition in a bounded domain. And as an application, we consider a free boundary problem for the Navier-Stokes equation. We prove a locally in time unique existence of solutions to this problem for any initial data and a globally in time unique existence of solutions to this problem for some small initial data.

    Original languageEnglish
    Pages (from-to)151-155
    Number of pages5
    JournalProceedings of the Japan Academy Series A: Mathematical Sciences
    Volume81
    Issue number9
    DOIs
    Publication statusPublished - 2005 Nov

    Fingerprint

    Maximal Regularity
    Incompressible Viscous Flow
    Free Surface
    Existence of Solutions
    Nonhomogeneous Boundary Conditions
    Regularity of Solutions
    Stokes Equations
    Neumann Problem
    Free Boundary Problem
    Bounded Domain
    Divergence
    Navier-Stokes Equations

    Keywords

    • Free boundary problem
    • Maximal regularity
    • Navier-Stokes equations
    • Neumann boundary condition
    • Stokes equations

    ASJC Scopus subject areas

    • Mathematics(all)

    Cite this

    L p-L q maximal regularity and viscous incompressible flows with free surface. / Shibata, Yoshihiro; Shimizu, Senjo.

    In: Proceedings of the Japan Academy Series A: Mathematical Sciences, Vol. 81, No. 9, 11.2005, p. 151-155.

    Research output: Contribution to journalArticle

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