Local exact controllability to the trajectories of theBoussinesq system via a fictitious control on the divergenceequation

Manuel González-Burgos; Sergio Guerrero; Jean Pierre Puel

doi:10.3934/cpaa.2009.8.311

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2009, Volume 8, Issue 1: 311-333. Doi: 10.3934/cpaa.2009.8.311

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Local exact controllability to the trajectories of the Boussinesq system via a fictitious control on the divergence equation

1.
Dpto. E.D.A.N., University of Sevilla, Aptdo. 1160, 41080 Sevilla
2.
Universite Pierre et Marie Curie-Paris6, UMR 7598 Laboratoire Jacques-Louis Lions, Paris, F-75005
3.
Laboratoire de Mathématiques de Versailles, Université de Versailles - St. Quentin, 45 Avenue des Etats Unis, 78035 Versailles

Received: March 31, 2008

Revised: July 31, 2008

Published: December 2008

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Abstract

In this paper, we deal with the three-dimensional Boussinesq system. We prove the local exact controllability to the trajectories of this system when the control is supported in a small set.

The main objective of this paper is to present a new method to control systems associated to equations of fluid dynamics. This method consists of controlling the same system with an additional control acting on the divergence condition in a first step and lifting this condition in a second step. In this paper, we have chosen to apply this technique to the Boussinesq system.

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Mathematics Subject Classification: Primary: 93C20, 76D55; Secondary: 93B05.

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Local exact controllability to the trajectories of the Boussinesq system via a fictitious control on the divergence equation

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