Optimal feedback control in the problem of the motion of a viscoelastic fluid

Abstract

We study an optimization problem for the feedback control system emerging as a regularized model for the motion of a viscoelastic fluid subject to the Jeffris-Oldroyd rheological relation. The approach includes systems governed by the classical Navier-Stokes equation as a particular case. Using the topological degree theory for condensing multimaps we prove the solvability of the approximating problem and demonstrate the convergence of approximate solutions to a solution of a regularized one. At last we show the existence of a solution minimizing a given convex, lower semicontinuous functional.