The problem of the flow of an ideal fluid with a singular sink at a depression on the bottom

Under consideration is a two-dimensional stationary problem concerning a flow of an ideal incompressible fluid bounded by an impenetrable bottom and a free surface from above. The flow is caused by a singular sink of a given strength that is located at the top of a triangular depression on the bottom. The problem is to determine the shape of the free boundary and the velocity field of the fluid. With the help of a conformal map and the Levi–Civita method, we rewrite the problem as an operator equation in some Hilbert space. We proved that, for the Froude number greater than some particular value, there is a solution of the problem.