On the unique solvability of a problem on water waves above submerged bodies

Abstract

Time-harmonic motion of an ideal unbounded fluid in the presence of rigid bodies located under fluid’s free surface is considered. New criteria for the unique solvability of the corresponding linear boundary-value problem are suggested. These criteria are based on the introduction of two compact self-adjoint integral operators and on the investigation of their eigenvalues and eigenfunctions. For the two-dimensional problem, an algorithm is developed for finding solutions to the homogeneous problem (the so-called trapped modes). Examples of numerical computations illustrating the theoretical results are given. Bibliography: 18 titles.