Optimal control of the two-dimensional stationary Naviers-Stokes equations with measure valued controls

Abstract

In this paper, we consider an optimal control problem for the two-dimensional stationary Navier-Stokes system. Looking for sparsity, we take Borel measures as controls. We prove the well-posedness of the control problem and derive necessary and sufficient conditions for local optimality of the controls. Finally, under a second order condition, we prove rates of the optimal states with respect to small perturbations in the data of the control problem.