Geodesic
Insensitizing controls with two vanishing components for the three-dimensional Boussinesq system
Carreño, N.1 ; Guerrero, S.1  ; Gueye, M.1 
1 UniversitéPierre et Marie Curie, UMR 7598, Laboratoire Jacques-Louis Lions, 75005 Paris, France.
ESAIM: Control, Optimisation and Calculus of Variations, Tome 21 (2015) no. 1, pp. 73-100

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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.

DOI : 10.1051/cocv/2014020
Classification : 34B15, 35Q30, 93C10, 93B05
Keywords: Navier−Stokes system, Boussinesq system, null controllability, Carleman inequalities, insensitizing controls

Carreño, N. 1 ; Guerrero, S. 1 ; Gueye, M. 1

1 UniversitéPierre et Marie Curie, UMR 7598, Laboratoire Jacques-Louis Lions, 75005 Paris, France. 
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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, Tome 21 (2015) no. 1, pp. 73-100. doi: 10.1051/cocv/2014020

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