Insensitizing controls for the Navier–Stokes equations

Gueye, Mamadou

doi:10.1016/j.anihpc.2012.09.005

Gueye, Mamadou

Annales de l'I.H.P. Analyse non linéaire, Tome 30 (2013) no. 5, pp. 825-844.

Résumé

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.

MR Zbl | 2 citations dans Numdam

DOI : 10.1016/j.anihpc.2012.09.005

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     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},
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     number = {5},
     year = {2013},
     doi = {10.1016/j.anihpc.2012.09.005},
     mrnumber = {3103172},
     zbl = {06295443},
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     url = {http://archive.numdam.org/articles/10.1016/j.anihpc.2012.09.005/}
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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://archive.numdam.org/articles/10.1016/j.anihpc.2012.09.005/

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