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Local exact controllability to the trajectories of the Navier-Stokes system withnonlinear Navier-slip boundary conditions

Published online by Cambridge University Press:  20 June 2006

Sergio Guerrero*
Affiliation:
Dpto. E.D.A.N., University of Sevilla, Aptdo. 1160, 41080 Sevilla, Spain; sguerrero@us.es.
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Abstract

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.

Type
Research Article
Copyright
© EDP Sciences, SMAI, 2006

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