Second-order sufficient optimality conditions for the optimal control of Navier-Stokes equations
Fredi Tröltzsch, Daniel Wachsmuth (2005)
ESAIM: Control, Optimisation and Calculus of Variations
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In this paper sufficient optimality conditions are established for optimal control of both steady-state and instationary 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 -neighborhood, whereby the underlying analysis allows to use weaker norms than .