The two-dimensional Neumann-Kelvin problem for an interface-intersecting body in a two-layer fluid

A two-dimensional body moves forward with constant velocity in an inviscid incompressible fluid under gravity. The fluid consists of two layers having different densities, and the body intersects an interface between the layers. The boundary-value problem for the velocity potential is considered in the framework of linearized water-wave theory. A pair of physically justified supplementary conditions is introduced at points where the body intersects the interface. The extended problem is shown to be well-posed and reduced to an integro-algebraic system. Total resistance to the body motion is found using the asymptotics of the solution at infinity