Optimal Feedback Control Problem for the Bingham Model with Periodical Boundary Conditions on Spatial Variables

The paper is devoted to an optimal feedback control problem for the Bingham model with periodic conditions on spatial variables. An interpretation of the problem is given in the form of operator inclusion with multivalued right-hand side. On the base of a topological approximation approach to studying hydrodynamics problems, and the degree theory of multivalued vector fields, the existence of solutions of this inclusion is deduced. Then it is proved that among the solutions of the problem in question, there is a solution minimizing a given cost functional.