On optimal control in a model of rigid-viscoplastic media with Dirichlet boundary conditions

In this paper, we consider the optimal control problem in a 3D flow model for incompressible rigid-viscoplastic media of the Bingham kind with homogeneous Dirichlet boundary conditions and a given cost functional. On the basis of methods of the theory of variational inequalities with pseudo-monotone operators, a theorem on the solvability of the optimization problem in the class of weak steady solutions is proved.