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This paper is concerned with boundary integral equation methods for solvingthe two-dimensional fluid-solid interaction problem. We reduce the problem tothree differential systems of boundary integral equations via direct andindirect approaches. Existence and uniqueness results for variational solutionsof boundary integral equations equations are established. Since in all theseboundary variational formulations, the hypersingular boundary integral operatorassociated with the time-harmonic Navier equation is a dominated integraloperator, we also include a new regularization formulation for thishypersingular operator, which allows us to treat the hypersingular kernel by awealkly singular kernel. Numerical examples are presented to verify andvalidate the theoretical results.

Boundary integral equation methods for the two dimensional fluid-solid interaction problem