In this paper, we deal with optimal boundary control for the Navier-Stokes problem. We establish the existence of such a control in appropriate functional spaces. Then we study a stabilization problem around a steady state. In view of numerical approximation, we derive rigorously Euler equations satisfied by the control.
"A variational approach for optimal control of the Navier-Stokes Equations." Adv. Differential Equations 15 (9/10) 829 - 852, September/October 2010.