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--Stokes equations},
journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
volume = {30},
year = {2013},
pages = {825-844},
doi = {10.1016/j.anihpc.2012.09.005},
mrnumber = {3103172},
zbl = {06295443},
language = {en},
url = {http://dml.mathdoc.fr/item/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) pp. 825-844. doi : 10.1016/j.anihpc.2012.09.005. http://gdmltest.u-ga.fr/item/AIHPC_2013__30_5_825_0/
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