SIAM Journal on Control and Optimization / Optimal control of the two-dimensional stationary navier-stokes equations with measure valued controls

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. European Research Council 668998 Accepted version