The authors consider an optimal control problem associated with the 3D Navier-Stokes system
where is a bounded domain with smooth boundary, is a control function. It is necessary to find a pair such that is the solution of (1) associated to and
with . Two results are obtained in the paper. First, the solutions of the optimal control problem generate a multivalued process which has a pullback attractor. Second, under the unproved assumption of strong global solvability of the 3D Navier-Stokes system the pullback attractor of the process coincides with the global attractor of the semiflow.