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ESAIM: Control, Optimisation and Calculus of Variations (1)

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Local exact controllability to the trajectoriesof the Navier-Stokes system withnonlinear Navier-slip boundary conditions
Sergio Guerrero
Journal:

ESAIM: Control, Optimisation and Calculus of Variations / Volume 12 / Issue 3 / July 2006

Published online by Cambridge University Press:

20 June 2006, pp. 484-544

Print publication:

July 2006
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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.