Weak solvability of non-linearly viscous Pavlovsky model

This paper is devoted to the solvability of one initial-boundary value problem describing the motion of aqueous polymers solutions. This model considers the non-linear viscosity of the fluid. The existence of weak solutions to the problem under consideration is proved on the base of the topological approximation approach. Also for the studied mathematical model the problem of optimal feedback control is considered. The existence of an optimal solution that gives a minimum to a given bounded and lower semicontinuous performance functional is proved.