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In this paper we consider the resolvent Stokes problem in the case there is asmall perturbation of the domain caused by a perturbed boundary. Firstly, weprove that the solution of Stokes problem is continuous due to this smallperturbation. Secondly, we derive the first-order term in the displacementfield perturbation that due to the deformation of the domain. It is worthemphasizing that even though only the first-order term is given, our methodenables us to derive higher-order terms as well. The derivation is rigorous andbased on layer potential techniques.

Asymptotic formula for the solution of the Stokes problem with a small perturbation of the domain in two and three dimensions