On Solutions of the One-Dimensional Goldshtik Problem

A one-dimensional analog of the mathematical model of separated flows of an incompressible Goldshtik fluid is considered. The model is a boundary value problem for a second-order ordinary differential equation with discontinuous right-hand side. Some properties of the solutions of the problem, as well as the properties of the energy functional for different values of vorticity, are established. An approximate solution of the boundary value problem under study is found using the shooting method.