Author(s) :
Fredi Troeltzsch
,
Daniel Wachsmuth
Preprint series of the Institute of Mathematics, Technische Universität Berlin
Preprint 30-2003
MSC 2000
- 49K20 Problems involving partial differential equations
-
49K27 Problems in abstract spaces
Abstract :
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 $L^\infty$.
Keywords :
Optimal control, Navier-Stokes equations, control constraints, second-order optimality conditions, first-order necessary conditions