On Uniqueness and Solvability in the Linear Problem of Ship Waves

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. We discuss the statement of the problem with some attention paid to the conditions at infinity. For the problem we derive Green’s identity and boundary Fredholm integral equations on the wetted surface of the bodies. Equivalence of the equations and the boundary 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 parameters of possible non-uniqueness parameters. Algorithms for verification of uniqueness are developed and numerical results illustrating the theoretical considerations are given.