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

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