In this paper, we deal with the existence of insensitizing controls for the Navier–Stokes equations in a bounded domain with Dirichlet boundary conditions. We prove that there exist controls insensitizing the -norm of the observation of the solution in an open subset of the domain, under suitable assumptions on the data. This problem is equivalent to an exact controllability result for a cascade system. First we prove a global Carleman inequality for the linearized Navier–Stokes system with right-hand side, which leads to the null controllability at any time . Then, we deduce a local null controllability result for the cascade system.
@article{AIHPC_2013__30_5_825_0, author = {Gueye, Mamadou}, title = {Insensitizing controls for the {Navier{\textendash}Stokes} equations}, journal = {Annales de l'I.H.P. Analyse non lin\'eaire}, pages = {825--844}, publisher = {Elsevier}, volume = {30}, number = {5}, year = {2013}, doi = {10.1016/j.anihpc.2012.09.005}, mrnumber = {3103172}, zbl = {06295443}, language = {en}, url = {http://www.numdam.org/articles/10.1016/j.anihpc.2012.09.005/} }
TY - JOUR AU - Gueye, Mamadou TI - Insensitizing controls for the Navier–Stokes equations JO - Annales de l'I.H.P. Analyse non linéaire PY - 2013 SP - 825 EP - 844 VL - 30 IS - 5 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.anihpc.2012.09.005/ DO - 10.1016/j.anihpc.2012.09.005 LA - en ID - AIHPC_2013__30_5_825_0 ER -
%0 Journal Article %A Gueye, Mamadou %T Insensitizing controls for the Navier–Stokes equations %J Annales de l'I.H.P. Analyse non linéaire %D 2013 %P 825-844 %V 30 %N 5 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.anihpc.2012.09.005/ %R 10.1016/j.anihpc.2012.09.005 %G en %F AIHPC_2013__30_5_825_0
Gueye, Mamadou. Insensitizing controls for the Navier–Stokes equations. Annales de l'I.H.P. Analyse non linéaire, Tome 30 (2013) no. 5, pp. 825-844. doi : 10.1016/j.anihpc.2012.09.005. http://www.numdam.org/articles/10.1016/j.anihpc.2012.09.005/
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