Insensitizing controls for the Boussinesq system with no control on the temperature equation

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Abstract

In this paper, we prove the existence of controls insensitizing the L2-norm of the solution of the Boussinesq system. The novelty here is that no control is used on the temperature equation. Furthermore, the control acting on the uid equation can be chosen to have one vanishing component. It is well known that the insensitizing control problem is equivalent to a null controllability result for a cascade system, which is obtained thanks to a suitable Carleman estimate for the adjoint of the linearized system and an inverse mapping theorem. The particular form of the adjoint equation will allow us to obtain the null controllability of the linearized system.
Original languageEnglish
Pages (from-to)235-258
Number of pages24
JournalAdvances in Differential Equations
Publication statusPublished - 1 Mar 2017

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