In this paper, we prove the existence of controls insensitizing the$L^2$-norm of the solution of the Boussinesq system. The novelty hereis that no control is used on the temperature equation. Furthermore,the control acting on the fluid equation can be chosen to have onevanishing component. It is well known that the insensitizing controlproblem is equivalent to a null controllability result for a cascadesystem, which is obtained thanks to a suitable Carleman estimate forthe adjoint of the linearized system and an inverse mapping theorem.The particular form of the adjoint equation will allow us to obtainthe null controllability of the linearized system.
"Insensitizing controls for theBoussinesq system withno control on the temperature equation." Adv. Differential Equations 22 (3/4) 235 - 258, March/April 2017.