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

Shuichi Jimbo, Hideo Kozono, Yoshiaki Teramoto, Erika Ushikoshi

Research output: Contribution to journalArticlepeer-review

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 R3. 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 T2.

Original languageEnglish
Pages (from-to)877-884
Number of pages8
JournalMathematische Annalen
Volume368
Issue number1-2
DOIs
Publication statusPublished - 2017 Jun 1
Externally publishedYes

Keywords

  • 35Q10

ASJC Scopus subject areas

  • Mathematics(all)

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