LOCAL EXACT CONTROLLABILITY TO THE TRAJECTORIES OF THE BOUSSINESQ SYSTEM VIA A FICTITIOUS CONTROL ON THE DIVERGENCE EQUATION

In this paper, we deal with the three-dimensional Boussinesq sys- tem. 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 ∞uid dynamics. This method consists of controlling the same system with an additional control acting on the divergence condition in a flrst 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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