Solvability of the boundary value problem for the stationary Boussinesq magnetic hydrodynamics model with variable leading coefficients

A boundary value problem for a stationary model of magnetic hydrodynamics of a viscous heat-conducting liquid with variable leading coefficients is investigated. The model under consideration consists of the Navier–Stokes equations, Maxwell's equations, generalized Ohm's law for a moving fluid, and the convection-diffusion equation for temperature, which are nonlinearly interconnected. Sufficient conditions are established for variable coefficients and other data to ensure the global solvability of the specified problem and the local uniqueness of its solution.