OPTIMAL CONTROLS OF NAVIER-STOKES EQUATIONS

This paper studies optimal control problems of the fluid flow governed by the Navier-Stokes equations. Two control problems are formulated in the case of the driven cavity and flow through a channel with sudden expansion and solved successfully using a numerical optimization algorithm based on the augmented Lagrangian method. Existence and the first-order optimality condition of the optimal control are established. A convergence result on the augmented Lagrangian method for nonsmooth cost functional is obtained.