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

作者：Thi Hong Cam Luong; Daveau Christian^*

来源：Complex Variables and Elliptic Equations, 2014, 59(9): 1269-1282.

DOI：10.1080/17476933.2013.831846

• Stokes problem
• asymptotic behaviour
• perturbation
• layer potentials
• Fredholm equation

In this paper, we consider the Stokes resolvent problem in the case when there is a small perturbation of the domain with C-2-boundary. Firstly, we prove that the solution of Stokes problem is continuous with respect to this small perturbation. Secondly, we derive the first-order term in the displacement field perturbation. 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.

• 出版日期2014