Hadamard Variational Formula for the Green's Function of the Boundary Value Problem on the Stokes Equations

Hideo Kozono, Erika Ushikoshi

    研究成果: Article

    6 引用 (Scopus)

    抄録

    For every ε > 0,we consider the Green's matrix Gε(x,y) of the Stokes equations describing the motion of incompressible fluids in a bounded domain Ωε ⊂ ℝd, which is a family of perturbation of domains from Ω ≡ Ω0 with the smooth boundary ∂Ω. Assuming the volume preserving property, that is, vol.Ωε = vol.Ω for all ε > 0, we give an explicit representation formula for δG(x,y) ≡ limε→+0 ε-1(Gε(x,y) - G0)) in terms of the boundary integral on ∂Ω of G0(x,y). Our result may be regarded as a classical Hadamard variational formula for the Green's functions of the elliptic boundary value problems.

    元の言語English
    ページ(範囲)1005-1055
    ページ数51
    ジャーナルArchive for Rational Mechanics and Analysis
    208
    発行部数3
    DOI
    出版物ステータスPublished - 2013

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    Green's Matrix
    Representation Formula
    Boundary Integral
    Stokes Equations
    Elliptic Boundary Value Problems
    Green's function
    Incompressible Fluid
    Boundary value problems
    Explicit Formula
    Bounded Domain
    Boundary Value Problem
    Perturbation
    Fluids
    Motion
    Family

    ASJC Scopus subject areas

    • Analysis
    • Mechanical Engineering
    • Mathematics (miscellaneous)

    これを引用

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    N2 - For every ε > 0,we consider the Green's matrix Gε(x,y) of the Stokes equations describing the motion of incompressible fluids in a bounded domain Ωε ⊂ ℝd, which is a family of perturbation of domains from Ω ≡ Ω0 with the smooth boundary ∂Ω. Assuming the volume preserving property, that is, vol.Ωε = vol.Ω for all ε > 0, we give an explicit representation formula for δG(x,y) ≡ limε→+0 ε-1(Gε(x,y) - G0)) in terms of the boundary integral on ∂Ω of G0(x,y). Our result may be regarded as a classical Hadamard variational formula for the Green's functions of the elliptic boundary value problems.

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