Preprint 22-2005

State-constrained optimal control of the stationary Navier-Stokes equations

Author(s) : Juan Carlos de los Reyes , Roland Griesse

Preprint series of the Institute of Mathematics, Technische Universität Berlin
Preprint 22-2005

MSC 2000

35Q35 Other equations arising in fluid mechanics

49J20 Optimal control problems involving partial differential equations

Abstract :
In this paper, the optimal control problem of the stationary Navier-Stokes equations in the presence of state constraints is investigated. We prove the existence of an optimal solution and derive first order necessary optimality conditions. The regularity of the adjoint state and the state constraint multiplier is also studied. Finally, the Lipschitz stability of the optimal control, state and adjoint variables with respect to perturbations is proved.

Keywords : Optimal control, Navier-Stokes equations, state constraints, Lipschitz stability