On uniqueness of solutions of control problems for the stationary model of viscous magnetic hydrodynamics

Control problems for the stationary model of viscous magnetic hydrodynamics under inhomogeneous boundary conditions for the velocity and electromagnetic field are considered. These problems consist of minimization of certain cost functionals dependent on weak solutions of the boundary value problems. The sufficient conditions of the regularity of the Lagrange multipliers and the local uniqueness of the solutions of the control problems are deduced.