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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 non- uniqueness can occur, are found.