ABSTRACT
The optimization control problems for the systems described by Navier–Stokes equations are the subject of the final chapter of Part III. We consider Navier–Stokes equations for the stationary and evolutional cases and with heat equations. At first, we analyze the properties of the considered boundary problems. Then we prove the existence of the optimal controls. Finally, we determine the necessary conditions of optimality by using the extended differentiability of control–state mapping.
