On uniqueness in the two- and three-dimensional Neumann-Kelvin problem

The uniqueness question for the classical Neumann Kelvin problem of the. linear theory of ship waves is considered. Both two- and three-dimensional problems are studied in the case when contours of ships are totally submerged. A new uniqueness theorem. valid for bodies of arbitrary shape and without assumptions on finiteness of energy, is proved. Simple bounds for the set of parameters, for which nonuniqueness can occur, are found.