Insensitizing controls for the Navier–Stokes equations
Annales de l'I.H.P. Analyse non linéaire, Volume 30 (2013) no. 5, p. 825-844
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 L 2 -norm of the observation of the solution in an open subset 𝒪 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 T>0. 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},
     publisher = {Elsevier},
     volume = {30},
     number = {5},
     year = {2013},
     pages = {825-844},
     doi = {10.1016/j.anihpc.2012.09.005},
     zbl = {06295443},
     mrnumber = {3103172},
     language = {en},
     url = {http://www.numdam.org/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, Volume 30 (2013) no. 5, pp. 825-844. doi : 10.1016/j.anihpc.2012.09.005. http://www.numdam.org/item/AIHPC_2013__30_5_825_0/

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