Local exact controllability to the trajectories of the Navier-Stokes system with nonlinear Navier-slip boundary conditions
ESAIM: Control, Optimisation and Calculus of Variations, Volume 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: 10.1051/cocv:2006006
Classification: 34B15, 35Q30, 76D03, 93B05, 93C10
Keywords: Navier-Stokes system, controllability, slip
Guerrero, Sergio 1

1 Laboratoire Jacques-Louis Lions, Université Pierre et Marie Curie, boîte courrier 187, 75035 Cedex 05, Paris, France;
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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, Volume 12 (2006) no. 3, pp. 484-544. doi : 10.1051/cocv:2006006. http://archive.numdam.org/articles/10.1051/cocv:2006006/

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