Hadamard variational formula for eigenvalues of the Stokes equations and its application

Shuichi Jimbo, Hideo Kozono, Yoshiaki Teramoto, Erika Ushikoshi

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    Abstract

    Based on the explicit representation of the Hadamard variational formula [1] for eigenvalues of the Stokes equations, we investigate the geometry of the domain in (Formula presented.). It turns out that if the first variation of some eigenvalue of the Stokes equations for all volume preserving perturbations vanishes, then the domain is necessarily diffeomorphic to the 2-dimensional torus (Formula presented.).

    Original languageEnglish
    Pages (from-to)1-8
    Number of pages8
    JournalMathematische Annalen
    DOIs
    Publication statusAccepted/In press - 2016 Apr 16

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    ASJC Scopus subject areas

    • Mathematics(all)

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