The optimal control problem for the model of dynamics of weakly viscoelastic fluid

In this article we study the optimal control of solutions of the Dirichlet–Showalter–Sidorov problem for the system of equations of Kelvin–Voight zero order fluid motion, which is called a system of Oskolkov equations. The case of the degenerate equation is considered. Existence of global in time weak generalized solution of the model in the space of solenoidal functions is proved. The existence of optimal control of weak generalized solutions of Showalter–Sidorov problem for abstract semilinear Sobolev type equation is shown. The obtained abstract results are applied to the Oskolkov model.