SECOND-ORDER SUFFICIENT OPTIMALITY CONDITIONS FOR THE OPTIMAL CONTROL OF NAVIER-STOKES EQUATIONS

摘要

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 L~s-neighborhood, whereby the underlying analysis allows to use weaker norms than L~∞.