Geodesic
Local exact controllability to the trajectories of the Navier-Stokes system with nonlinear Navier-slip boundary conditions
Guerrero, Sergio1 
1 Laboratoire Jacques-Louis Lions, Université Pierre et Marie Curie, boîte courrier 187, 75035 Cedex 05, Paris, France;
ESAIM: Control, Optimisation and Calculus of Variations, Tome 12 (2006) no. 3, pp. 484-544

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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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     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},
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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

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