Control theory
Controllability to trajectories of a Ladyzhenskaya model for a viscous incompressible fluid
Comptes Rendus. Mathématique, Volume 359 (2021) no. 6, pp. 719-732.

We consider the controllability of a viscous incompressible fluid modeled by the Navier–Stokes system with a nonlinear viscosity. To prove the controllability to trajectories, we linearize around a trajectory and the corresponding linear system includes a nonlocal spatial term. Our main result is a Carleman estimate for the adjoint of this linear system. This estimate yields in a standard way the null controllability of the linear system and the local controllability to trajectories. Our method to obtain the Carleman estimate is completely general and can be adapted to other parabolic systems when a Carleman estimate is available.

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DOI: 10.5802/crmath.202
Classification: 76D05, 93C20, 93B05, 93B07
Guerrero, Sergio 1; Takahashi, Takéo 2

1 Sorbonne Université, Université Paris-Diderot, CNRS, LJLL, F-75005 Paris, France
2 Université de Lorraine, CNRS, Inria, IECL, F-54000 Nancy, France
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Guerrero, Sergio; Takahashi, Takéo. Controllability to trajectories of a Ladyzhenskaya model for a viscous incompressible fluid. Comptes Rendus. Mathématique, Volume 359 (2021) no. 6, pp. 719-732. doi : 10.5802/crmath.202. http://www.numdam.org/articles/10.5802/crmath.202/

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