Second-order sufficient optimality conditions for the optimal control of navier-stokes equations

Abstract

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 Ls-neighborhood, whereby the underlying analysis allows to use weaker norms than L ∞. © EDP Sciences, SMAI 2006.