On the statement of the three-dimensional Neumann-Kelvin problem

The classical three-dimensional Neumann-Kelvin problem of the linear theory of ship waves is considered and its statement is investigated with particular attention to the conditions at infinity. The general eigensolution to the problem in empty half-space (in absence of bodies) is derived. This solution allows us to formulate correct conditions at infinity both for the Green function and for the potential of the problem, describing motion of submerged bodies.