Methods of non-smooth analysis in problems of fluid dynamic

The purpose of this research is to construct a solution of the boundary value problem for a system of nonlinear partial differential equations that simulates the quasi-geostrophic motion in the layer of an ideal incompressible electrically conductive fluid enclosed between space-changing and time-varying surfaces, taking into account inertial forces. Assuming that the Rossby numbers, which are a measure of the local and advective accelerations to the acceleration of Coriolis, of the same order, the problem reduces to solving a system of three nonlinear equations for hydromagnetic pressure and for two functions describing the magnetic field. For an infinitely extended horizontally conducting electrically conducting liquid under the assumption of approximate constancy the slope of the surface, bounding the layer from above, the exact solution of the system of the corresponding nonlinear equations and the dispersion relation. In the actual form shows the main characteristics of the movement.