On Uniqueness and Solvability in The Linear Problem of Ship Waves

Abstract

This work is devoted to the question of uniqueness and solvability for the linear problem of ship waves, describing the forward motion of rigid totally submerged bodies in an unbounded fluid with a free surface. The statement of the problem is discussed with some attention paid to the conditions at infinity. For the problem, Green's identity and boundary integral equations on the wetted surface of the bodies are derived; equivalence of the equations and the boundary-value problem is proved. New criteria and sufficient conditions of unique solvability are suggested. A uniqueness theorem is proved in the form of simple bounds of possible nonuniqueness parameters. Algorithms for verification of uniqueness and finding nonuniqueness examples are developed and numerical results illustrating the theoretical considerations are given.