On the control of some coupled systems of the Boussinesq kind with few controls

Enrique Fernández-Cara; Diego A. Souza

doi:10.3934/mcrf.2012.2.121

Article Contents

2012, Volume 2, Issue 2: 121-140. Doi: 10.3934/mcrf.2012.2.121

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On the control of some coupled systems of the Boussinesq kind with few controls

Enrique Fernández-Cara^1, and
Diego A. Souza^2,

1.
Departamento de Ecuaciones Diferenciales y Análisis Numérico, Universidad de Sevilla, Aptdo. 1160, 41080 Sevilla
2.
Dpto. de Matemática, Universidade Federal da Paraba, 58051-900, João Pessoa

Received: February 2011

Revised: September 2011

Published: June 2012

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Abstract

This paper is devoted to prove the local exact controllability to the trajectories for a coupled system, of the Boussinesq kind, with a reduced number of controls. In the state system, the unknowns are the velocity field and pressure of the fluid $(\mathbf{y},p)$, the temperature $\theta$ and an additional variable $c$ that can be viewed as the concentration of a contaminant solute. We prove several results, that essentially show that it is sufficient to act locally in space on the equations satisfied by $\theta$ and $c$.

Keywords:

Navier-Stokes and Boussinesq-like systems,
controllability,
control reduction.

Mathematics Subject Classification: Primary: 35B37, 93B05; Secondary: 35Q35.

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References

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