1304.2609 (T. H. C Luong et al.)

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

T. H. C Luong, C. Daveau

In this paper we consider the resolvent Stokes problem in the case there is a small perturbation of the domain caused by a perturbed boundary. Firstly, we prove that the solution of Stokes problem is continuous due to this small perturbation. Secondly, we derive the first-order term in the displacement field perturbation that due to the deformation of the domain. It is worth emphasizing that even though only the first-order term is given, our method enables us to derive higher-order terms as well. The derivation is rigorous and based on layer potential techniques.

View original: http://arxiv.org/abs/1304.2609