Second-order sufficient optimality conditions for the optimal control of Navier-Stokes equations

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Author(s) : Fredi Troeltzsch , Daniel Wachsmuth

Preprint series of the Institute of Mathematics, Technische Universität Berlin
Preprint 30-2003

MSC 2000

49K20 Problems involving partial differential equations
49K27 Problems in abstract spaces

Abstract :
In this paper sufficient optimality conditions are established for optimal control of both steady-state and evolution Navier-Stokes equations. The second-order condition requires coercivity of the Lagrange function on a suitable subspace together with first-order necessary conditions. It ensures local optimality of a reference function in a $L^s$-neighborhood, whereby the underlying analysis allows to use weaker norms than $L^\infty$.

Keywords : Optimal control, Navier-Stokes equations, control constraints, second-order optimality conditions, first-order necessary conditions