Abstract
In this paper we construct a dynamical process (in general, multivalued) generated by the set of solutions of an optimal control problem for the three-dimensional Navier–Stokes system. We prove the existence of a pullback attractor for such multivalued process. Also, we establish the existence of a uniform global attractor containing the pullback attractor. Moreover, under the unproved assumption that strong globally defined solutions of the three-dimensional Navier–Stokes system exist, which guaranties the existence of a global attractor for the corresponding multivalued semiflow, we show that the pullback attractor of the process coincides with the global attractor of the semiflow.
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