Stationary simple waves on a barotropic liquid shear flow

Stationary three-dimensional flows of a barotropic liquid in a gravity field are considered. In the shallow-water approximation, the Euler equations are transformed into a system of integrodifferential equations by the Euler–Lagrange change of coordinates. A system of simple-wave equations is obtained, for which the theorem of existence of a solution attached to a given shear flow is proved. As an example, a particular solution analogous to the solution of the problem of a gas flow around a convex angle is given.