On Nusselt’s solution and its generalizations

The paper presents the solution of problems generalizing Nusselt classical solution, which describes the steady flow of viscous liquid on an inclined plane. First, it is a stationary two-layer flow. Secondly, these are analogous unsteady motions. In the latter case, the solutions are found by the Laplace transform method. It is proved that with increasing time, these solutions tend to stationary. It has been established that all new solutions uniquely determined by the initial and boundary conditions.