Flow control with regularized state constraints

Abstract

We consider the distributed optimal control of the Navier-Stokes equations in presence of pointwise state constraints. A Lavrentiev regularization of the constraints is proposed and a first order optimality system is derived. The regularity of the mixed constraint multiplier is investigated and second order sufficient optimality conditions are studied. In the last part of the paper, a semi-smooth Newton method is applied for the numerical solution of the control problem and numerical experiments are carried out. © 2007 Springer-Verlag Berlin Heidelberg.