Asymptotic behaviors for eigenvalues and eigenfunctions associated to Stokes operator in the presence of small boundary perturbations

We consider the Stokes eigenvalue problem in a bounded domain of R3 with Dirich- let boundary conditions. The aim of this paper is to advance the development of high-order terms in the asymptotic expansions of the boundary perturbations of eigen- values, eigenfunctions and eigenpressures for the Stokes operator caused by small per- turbations of the boundary. Our derivation is rigorous and proved by layer potential techniques.