# American Institute of Mathematical Sciences

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

 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

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.
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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