### 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 language | English |
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Pages (from-to) | 1-8 |

Number of pages | 8 |

Journal | Mathematische Annalen |

DOIs | |

Publication status | Accepted/In press - 2016 Apr 16 |

### ASJC Scopus subject areas

- Mathematics(all)

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## Cite this

Jimbo, S., Kozono, H., Teramoto, Y., & Ushikoshi, E. (Accepted/In press). Hadamard variational formula for eigenvalues of the Stokes equations and its application.

*Mathematische Annalen*, 1-8. https://doi.org/10.1007/s00208-016-1410-5