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Preprint 32-2005

Optimal control of the stationary Navier-Stokes equations with mixed control-state constraints

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Author(s) : Juan Carlos de los Reyes , Fredi Tröltzsch

Preprint series of the Institute of Mathematics, Technische Universität Berlin
Preprint 32-2005

MSC 2000

49K20 Problems involving partial differential equations
76D05 Navier-Stokes equations

Abstract :
In this paper we consider the distributed optimal control of the Navier-Stokes equations in presence of pointwise mixed control-state constraints. After deriving a first order necessary condition, the regularity of the mixed constraint multiplier is investigated. Second-order sufficient optimality conditions are studied as well. In the last part of the paper, a semi-smooth Newton method is applied for the numerical solution of the control problem. The convergence of the method is proved and numerical experiments are carried out.

Keywords : Optimal control, Navier-Stokes equations, mixed control-state constraints

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