A BOUNDARY CONTROL PROBLEM FOR VORTICITY MINIMIZATION IN TIME-DEPENDENT 2D NAVIER-STOKES EQUATIONS

Abstract. We deal with a boundary control problem for the vor-ticity minimization, in which the flow is governed by the time-dependent two dimensional incompressible Navier-Stokes equations. We derive a mathematical formulation and a process for an appro-priate control along the portion of the boundary to minimize the vorticity motion due to the flow in the fluid domain. After showing the existence of an optimal solution, we derive the optimality system for which optimal solutions may be determined. The differentiabil-ity of the state solution in regard to the control parameter shall be conjunct with the necessary conditions for the optimal solutions. 1