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

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.