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

Published online by Cambridge University Press:  20 June 2006

Sergio Guerrero
Sergio Guerrero*
Affiliation:
Dpto. E.D.A.N., University of Sevilla, Aptdo. 1160, 41080 Sevilla, Spain; [email protected].
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Abstract

In this paper we deal with the local exact controllability of theNavier-Stokes system with nonlinear Navier-slip boundaryconditions and distributed controls supported in small sets. In afirst step, we prove a Carleman inequality for the linearizedNavier-Stokes system, which leads to null controllability of thissystem at any time T>0. Then, fixed point arguments lead to thededuction of a local result concerning the exact controllabilityto the trajectories of the Navier-Stokes system.

Keywords

Navier-Stokes systemcontrollabilityslip.
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 12 , Issue 3 , July 2006 , pp. 484 - 544
Copyright
© EDP Sciences, SMAI, 2006

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