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

Published online by Cambridge University Press:  15 December 2005

Fredi Tröltzsch  and
Daniel Wachsmuth
Fredi Tröltzsch
Affiliation:
Institut für Mathematik, Technische Universität Berlin, Str. d. 17. Juni 136, 10632 Berlin, Germany; troeltz@math.tu-berlin.de; wachsmut@math.tu-berlin.de
Daniel Wachsmuth
Affiliation:
Institut für Mathematik, Technische Universität Berlin, Str. d. 17. Juni 136, 10632 Berlin, Germany; troeltz@math.tu-berlin.de; wachsmut@math.tu-berlin.de
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Abstract

In this paper sufficient optimality conditions are established for optimal control ofboth steady-state and instationary Navier-Stokes equations. The second-order condition requirescoercivity of the Lagrange function on a suitable subspace together with first-order necessaryconditions. It ensures local optimality of a reference function in a Ls -neighborhood, whereby the underlying analysis allows to use weaker norms than L∞ .

Keywords

Optimal controlNavier-Stokes equationscontrol constraintssecond-orderoptimality conditionsfirst-order necessary conditions.

Information

Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 12 , Issue 1 , January 2006 , pp. 93 - 119
Copyright
© EDP Sciences, SMAI, 2006

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