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arXiv · 1304.2609

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

T. H. C Luong·C. Daveau
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Abstract

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.

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T. H. C Luong, C. Daveau. 2013-04-09. Asymptotic formula for the solution of the Stokes problem with a small perturbation of the domain in two and three dimensions. https://arxiv.org/abs/1304.2609

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