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The aim of this paper is to establish necessary optimality conditions for optimal control problems governed by steady, incompressible Navier-Stokes equations with shear-dependent viscosity. The main difficulty derives from the fact that equations of this type may exhibit non-uniqueness of weak solutions, and is overcome by introducing a family of approximate control problems governed by well posed generalized Stokes systems and by passing to the limit in the corresponding optimality conditions.
@article{COCV_2013__19_1_219_0,
author = {Arada, Nadir},
title = {Distributed control for multistate modified {Navier-Stokes} equations},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
pages = {219--238},
publisher = {EDP-Sciences},
volume = {19},
number = {1},
year = {2013},
doi = {10.1051/cocv/2012007},
mrnumber = {3023067},
zbl = {1259.49028},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1051/cocv/2012007/}
}
TY - JOUR AU - Arada, Nadir TI - Distributed control for multistate modified Navier-Stokes equations JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2013 SP - 219 EP - 238 VL - 19 IS - 1 PB - EDP-Sciences UR - http://geodesic.mathdoc.fr/articles/10.1051/cocv/2012007/ DO - 10.1051/cocv/2012007 LA - en ID - COCV_2013__19_1_219_0 ER -
%0 Journal Article %A Arada, Nadir %T Distributed control for multistate modified Navier-Stokes equations %J ESAIM: Control, Optimisation and Calculus of Variations %D 2013 %P 219-238 %V 19 %N 1 %I EDP-Sciences %U http://geodesic.mathdoc.fr/articles/10.1051/cocv/2012007/ %R 10.1051/cocv/2012007 %G en %F COCV_2013__19_1_219_0
Arada, Nadir. Distributed control for multistate modified Navier-Stokes equations. ESAIM: Control, Optimisation and Calculus of Variations, Tome 19 (2013) no. 1, pp. 219-238. doi: 10.1051/cocv/2012007
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