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

Tröltzsch, Fredi; Wachsmuth, Daniel

Preprint-Reihe des Instituts für Mathematik, Technische Universität Berlin

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 $L^\infty$.