Solvability of a Boundary Value Problem for the Stationary Magnetohydrodynamics–Boussinesq Model with Variable Leading Coefficients

A boundary value problem for a stationary model of magnetohydrodynamics of a viscous heat-conducting fluid with variable leading coefficients is investigated. The model consists of the Navier–Stokes equations, Maxwell’s equations, the generalized Ohm law for a moving fluid, and a convection–diffusion equation for temperature. These equations are nonlinearly related to each other. Sufficient conditions on the variable coefficients and other data are established under which the problem is globally solvable and its solution is locally unique.