Volume 12, Number 3, July 2006
|Page(s)||484 - 544|
|Published online||20 June 2006|
Local exact controllability to the trajectories of the Navier-Stokes system with nonlinear Navier-slip boundary conditions
Dpto. E.D.A.N., University of Sevilla,
Aptdo. 1160, 41080 Sevilla, Spain; firstname.lastname@example.org.
Revised: 19 April 2005
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.
Mathematics Subject Classification: 34B15 / 35Q30 / 76D03 / 93B05 / 93C10
Key words: Navier-Stokes system / controllability / slip.
© EDP Sciences, SMAI, 2006
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