In this paper we prove the existence of insensitizing controls for a viscous newtonian fluid wherein thermic effects are taken into acount, the so called Boussinesq system. The proof relies on a standard approach introduced by Fursikov and Imanuvilov for the Navier−Stokes system which consists in solving a constrained extremal problem, and then on an inverse mapping theorem to deal with the nonlinear system. Furthermore, we use the coupling with the heat equation to get rid of two components of the control in the fluid equations.
Keywords: Navier−Stokes system, Boussinesq system, null controllability, Carleman inequalities, insensitizing controls
@article{COCV_2015__21_1_73_0, author = {Carre\~no, N. and Guerrero, S. and Gueye, M.}, title = {Insensitizing controls with two vanishing components for the three-dimensional {Boussinesq} system}, journal = {ESAIM: Control, Optimisation and Calculus of Variations}, pages = {73--100}, publisher = {EDP-Sciences}, volume = {21}, number = {1}, year = {2015}, doi = {10.1051/cocv/2014020}, mrnumber = {3348416}, zbl = {1315.35158}, language = {en}, url = {http://archive.numdam.org/articles/10.1051/cocv/2014020/} }
TY - JOUR AU - Carreño, N. AU - Guerrero, S. AU - Gueye, M. TI - Insensitizing controls with two vanishing components for the three-dimensional Boussinesq system JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2015 SP - 73 EP - 100 VL - 21 IS - 1 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/cocv/2014020/ DO - 10.1051/cocv/2014020 LA - en ID - COCV_2015__21_1_73_0 ER -
%0 Journal Article %A Carreño, N. %A Guerrero, S. %A Gueye, M. %T Insensitizing controls with two vanishing components for the three-dimensional Boussinesq system %J ESAIM: Control, Optimisation and Calculus of Variations %D 2015 %P 73-100 %V 21 %N 1 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/cocv/2014020/ %R 10.1051/cocv/2014020 %G en %F COCV_2015__21_1_73_0
Carreño, N.; Guerrero, S.; Gueye, M. Insensitizing controls with two vanishing components for the three-dimensional Boussinesq system. ESAIM: Control, Optimisation and Calculus of Variations, Volume 21 (2015) no. 1, pp. 73-100. doi : 10.1051/cocv/2014020. http://archive.numdam.org/articles/10.1051/cocv/2014020/
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