Exact solutions of the problem of free-boundary unsteady flows
arXiv:1210.2197 · doi:10.1016/j.crme.2013.02.009
Abstract
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 πis 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.