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arXiv · 1207.3255

Insensitizing controls for the Navier-Stokes equations

Mamadou Gueye
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Abstract

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 $\mathcal{O}$ 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.

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Mamadou Gueye. 2012-07-13. Insensitizing controls for the Navier-Stokes equations. https://doi.org/10.1016/j.anihpc.2012.09.005

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