Error estimates for an unregularized optimal control problem for the stationary Navier-Stokes equations
Provides theoretical foundations for optimal control of fluid flows, but the results are incremental and specific to the unregularized setting.
The paper proves existence, optimality conditions, and a priori error estimates for an unregularized optimal control problem governed by the stationary Navier-Stokes equations, focusing on bang-bang controls.
We consider an unregularized optimal control problem subject to the steady-state Navier-Stokes equations. We derive the existence of optimal solutions and prove first- and -- necessary and sufficient -- second-order optimality conditions. To approximate solutions to the optimal control problem, we consider the variational discretization scheme. We analyze convergence properties of the discretization and prove a priori error estimates for locally optimal controls that are nonsingular and which satisfy a growth condition which implies a bang-bang structure.