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We prove the null controllability in large time of the following linear parabolic equation involving the Grushin operator with an inversesquare potential ut − Δxu − |x| 2 Δyu − μ |x| 2 u = v1ω in a bounded domain Ω = Ω1 × Ω2 ⊂ R N 1 × R N 2 (N1 ≥ 3, N2 ≥ 1) intersecting the surface {x = 0} under an additive control supported in an open subset ω = ω1 × Ω2 of Ω.

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In this paper we prove the exact controllability to trajectories of the magneto-micropolar fluid equations with distributed controls. We first establish new Carleman inequalities for the associated linearized system which lead to its null controllability. Then, combining the null controllability of the linearized system with an inverse mapping theorem, we deduce the local exact controllability to trajactories of the nonlinear problem. 2000 Mathematics Subject Classification. 93B05, 35Q35, 93C20. Key words and phrases. Magneto-micropolar fluid, local controllability to trajectories, Carleman inequality, inverse mapping theorem.