The integral equation method for the 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 intersection interface between the layers. The boundary value problem for the velocity potential is considered in the framework of linearized water-wave theory. The problem is augmented by a pair of physically justified supplementary conditions at points where the body intersects the interface. The extended problem is reduced to an integro-algebraic system. The solvability of the system is proved