Existence of a solution of a modification of a system of equations of magnetohydrodynamics

The time-dependent system of equations describing plane-parallel motion of Ostwald–de Waele media is considered in the approximation of magnetohydrodynamics. The system differs from the classical equations of magnetohydrodynamics by the presence in the leading term of power nonlinearities. The initial boundary value problem is solved with the conditions of diffraction of the physical characteristics on the boundary separating the media. Existence of a generalized solution is proved on the basis of the Faedo–Galerkin method and the method of monotone operators.