Correctness Analysis of a Boundary Value Problemfor Stationary Magnetohydrodynamics Equations with Variable Coefficients

We study a boundary value problem for stationary equations of magnetohydrodynamics of a viscous heat-conducting fluid with variable coefficients considered under the Dirichlet condition for the velocity and mixed boundary conditions for the electromagnetic field and temperature. Sufficient conditions on the problem data providing the global solvability of the problem and the local stability of its solution are established.