Optimal feedback control problem for the Bingam model with periodical boundary conditions on spatial variables

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