Solvability of a boundary value problem for stationary equations of magnetohydrodynamics of a viscous heat-conducting fluid

We study a boundary value problem for the stationary equations of magnetohydrodynamics of a viscous heat-conducting fluid considered under the Dirichlet condition for the velocity and mixed boundary conditions for the electromagnetic field and the temperature. Sufficient conditions are established on the initial data that guarantee the global solvability of this problem and the local uniqueness of its solution.