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