A semi-smooth Newton method for control constrained boundary optimal control of the Navier-Stokes equations

In this paper we study optimal control of the Navier-Stokes equations when the control acts as a pointwise constrained boundary condition of Dirichlet type. The problem is analyzed in the control space H001/2, the optimality system and second order sufficient optimality conditions are derived. For the numerical solution we apply a semi-smooth Newton method to a regularized version of the original problem and show convergence properties of the method and of the regularized solutions towards the original one.