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 -neighborhood, whereby the underlying analysis allows to use weaker norms than .
Mots-clés : optimal control, Navier-Stokes equations, control constraints, second-order optimality conditions, first-order necessary conditions
@article{COCV_2006__12_1_93_0,
author = {Tr\"oltzsch, Fredi and Wachsmuth, Daniel},
title = {Second-order sufficient optimality conditions for the optimal control of {Navier-Stokes} equations},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
pages = {93--119},
publisher = {EDP-Sciences},
volume = {12},
number = {1},
year = {2006},
doi = {10.1051/cocv:2005029},
mrnumber = {2192070},
zbl = {1111.49017},
language = {en},
url = {http://www.numdam.org/articles/10.1051/cocv:2005029/}
}
TY - JOUR AU - Tröltzsch, Fredi AU - Wachsmuth, Daniel TI - Second-order sufficient optimality conditions for the optimal control of Navier-Stokes equations JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2006 SP - 93 EP - 119 VL - 12 IS - 1 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/cocv:2005029/ DO - 10.1051/cocv:2005029 LA - en ID - COCV_2006__12_1_93_0 ER -
%0 Journal Article %A Tröltzsch, Fredi %A Wachsmuth, Daniel %T Second-order sufficient optimality conditions for the optimal control of Navier-Stokes equations %J ESAIM: Control, Optimisation and Calculus of Variations %D 2006 %P 93-119 %V 12 %N 1 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/cocv:2005029/ %R 10.1051/cocv:2005029 %G en %F COCV_2006__12_1_93_0
Tröltzsch, Fredi; Wachsmuth, Daniel. Second-order sufficient optimality conditions for the optimal control of Navier-Stokes equations. ESAIM: Control, Optimisation and Calculus of Variations, Tome 12 (2006) no. 1, pp. 93-119. doi : 10.1051/cocv:2005029. http://www.numdam.org/articles/10.1051/cocv:2005029/
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