On a Stationary Problem of the Stokes Equation in an Infinite Layer in Sobolev and Besov Spaces

Takayuki Abe, Masao Yamazaki

    Research output: Contribution to journal › Article

    1 Citation (Scopus)

    Abstract

    This paper is concerned with the stationary problem of the Stokes equation in an infinite layer and provides a condition on the external force sufficient for the existence of the solution. Since the Poiseuille flow is a solution to the homogeneous equation, the solution is not unique when p = ∞. It is also proved that, under some suitable conditions, solutions to the homogeneous equation are limited only to the Poiseuille flow.

    Original languageEnglish
    Pages (from-to)61-100
    Number of pages40
    JournalJournal of Mathematical Fluid Mechanics
    Volume12
    Issue number1
    DOIs
    Publication statusPublished - 2010 Mar

    Fingerprint

    Sobolev space
    Poiseuille Flow
    Stokes Equations
    Besov Spaces
    Sobolev Spaces
    laminar flow
    Sufficient

    Keywords

    • Besov space
    • Homogeneous Besov space
    • Infinite layer
    • Poiseuille flow
    • Sobolev space
    • Stationary problem
    • Stokes equation

    ASJC Scopus subject areas

    • Applied Mathematics
    • Mathematical Physics
    • Computational Mathematics
    • Condensed Matter Physics

    Cite this

    On a Stationary Problem of the Stokes Equation in an Infinite Layer in Sobolev and Besov Spaces. / Abe, Takayuki; Yamazaki, Masao.

    In: Journal of Mathematical Fluid Mechanics, Vol. 12, No. 1, 03.2010, p. 61-100.

    Research output: Contribution to journal › Article

    Abe, T & Yamazaki, M 2010, 'On a Stationary Problem of the Stokes Equation in an Infinite Layer in Sobolev and Besov Spaces', Journal of Mathematical Fluid Mechanics, vol. 12, no. 1, pp. 61-100. https://doi.org/10.1007/s00021-008-0276-z
    Abe T, Yamazaki M. On a Stationary Problem of the Stokes Equation in an Infinite Layer in Sobolev and Besov Spaces. Journal of Mathematical Fluid Mechanics. 2010 Mar;12(1):61-100. https://doi.org/10.1007/s00021-008-0276-z
    Abe, Takayuki ; Yamazaki, Masao. / On a Stationary Problem of the Stokes Equation in an Infinite Layer in Sobolev and Besov Spaces. In: Journal of Mathematical Fluid Mechanics. 2010 ; Vol. 12, No. 1. pp. 61-100.
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