Asymptotics of the flows of a liquid with a free boundary with vanishing viscosity

The Navier-Stokes equations with vanishing viscosity are applied to the two-dimensional nonlinear problem of the flow of an incompressible fluid with a free surface, between porous walls. The problem is solved for large Reynolds numbers, and asymptotic expansions of the solution are obtained, in which the principal terms are defined by the corresponding flow of an ideal fluid. The solutions of the boundary layer problems describe the flow near the flow boundaries. The influence of low viscosity on the flow of a circular jet between moving walls is analyzed.