Exact solutions of the problem of free-boundary unsteady flows
  Some approach to the solution of boundary value problems for finding functions, which are analytical in a wedge, is proposed. If the ratio of the angle at the wedge vertex to a number \pi is rational, then the boundary value problem is reduced to the finite system of ordinary differential equations. Such approach, applied the problem of inertial motion of a liquid wedge, made it possible to sum series with small denominators arising in the problem and find four exact examples of self-similar flows with a free boundary. 
E.A. Karabut
physics.flu-dyn