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

TL;DR

This paper develops high-order asymptotic expansions for eigenvalues and eigenfunctions of the Stokes operator in a 3D domain with small boundary perturbations, using layer potential techniques.

Contribution

It provides rigorous derivations of high-order asymptotic terms for boundary perturbations affecting the Stokes eigenvalues and eigenfunctions.

Findings

High-order asymptotic expansions derived

Layer potential techniques used for rigorous proofs

Results applicable to small boundary perturbations in fluid dynamics

Abstract

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.