Local exact controllability to the trajectories of the Navier-Stokes system with nonlinear Navier-slip boundary conditions
ESAIM: Control, Optimisation and Calculus of Variations, Tome 12 (2006) no. 3, pp. 484-544.

In this paper we deal with the local exact controllability of the Navier-Stokes system with nonlinear Navier-slip boundary conditions and distributed controls supported in small sets. In a first step, we prove a Carleman inequality for the linearized Navier-Stokes system, which leads to null controllability of this system at any time $T>0$. Then, fixed point arguments lead to the deduction of a local result concerning the exact controllability to the trajectories of the Navier-Stokes system.

DOI : https://doi.org/10.1051/cocv:2006006
Classification : 34B15,  35Q30,  76D03,  93B05,  93C10
Mots clés : Navier-Stokes system, controllability, slip
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author = {Guerrero, Sergio},
title = {Local exact controllability to the trajectories of the {Navier-Stokes} system with nonlinear {Navier-slip} boundary conditions},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
pages = {484--544},
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Guerrero, Sergio. Local exact controllability to the trajectories of the Navier-Stokes system with nonlinear Navier-slip boundary conditions. ESAIM: Control, Optimisation and Calculus of Variations, Tome 12 (2006) no. 3, pp. 484-544. doi : 10.1051/cocv:2006006. http://www.numdam.org/articles/10.1051/cocv:2006006/

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