| Issue |
ESAIM: COCV
Volume 12, Number 3, July 2006
|
|
|---|---|---|
| Page(s) | 484 - 544 | |
| DOI | https://doi.org/10.1051/cocv:2006006 | |
| 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; sguerrero@us.es.
Received:
9
February
2004
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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