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

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∞ .

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