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This note deals with the local exact controllability to a particular class oftrajectories for the Boussinesq system with nonlinear Navier-slip boundaryconditions and internal controls having vanishing components. Briefly speaking,in two dimensions, the local exact controllability property is obtained usingonly one control in the heat equation, meanwhile two scalar controls arerequired in three dimensions.

Remarks on local controllability for the Boussinesq system with Navier boundary condition