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

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January 2009, 8(1): 311-333. doi: 10.3934/cpaa.2009.8.311

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

Manuel González-Burgos ^1, , Sergio Guerrero ^2, and Jean Pierre Puel ^3,

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, France
3.	Laboratoire de Mathématiques de Versailles, Université de Versailles - St. Quentin, 45 Avenue des Etats Unis, 78035 Versailles

Received April 2008 Revised August 2008 Published October 2008

Abstract
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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.

Keywords: Boussinesq system, Controllability, fictitious control, control of fluid flows.

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

Citation: Manuel González-Burgos, Sergio Guerrero, Jean Pierre Puel. Local exact controllability to the trajectories of the Boussinesq system via a fictitious control on the divergence equation. Communications on Pure & Applied Analysis, 2009, 8 (1) : 311-333. doi: 10.3934/cpaa.2009.8.311

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