Second-Order Optimality Conditions and Solution Stability to Optimal Control Problems Governed by Stationary Navier-Stokes Equations

In this paper, a class of parametric optimal control problems governed by stationary Navier-Stokes equations with mixed pointwise constraints is considered. We give no-gap second-order necessary and sufficient conditions for unperturbed problem. We show that if the strictly second-order sufficient condition for unperturbed problem is valid and the objective function is locally Lipschitz continuous, then the solution map is locally upper Holder continuous at the reference parameter.