The Neumann]Kelvin Problem for a Beam

We discuss existence, uniqueness and regularity of the solution of the plane Neumann]Kelvin problem in a strip, in the case of a beam. The problem is obtained by linearization of the equations of the wave-resistance problem for a ‘‘slender’’ cylinder semisubmerged in a heavy fluid and moving at uniform, supercritical speed in the direction orthogonal to its generators. The results obtained may be relevant for the resolution of the nonlinear wave-resistance problem.