Null controllability in large time of a parabolic equation involving the Grushin operator with an inverse-square potential

We prove the null controllability in large time of the following linear parabolic equation involving the Grushin operator with an inverse-square potential

$$u_t-Delta_{x} u-|x|^{2}Delta_{y}u-frac{mu}{|x|^2}u=v1_omega$$

in a bounded domain ({Omega=Omega_1times Omega_2subset mathbb{R}^{N_1}times mathbb{R}^{N_2} (N_1geq 3, N_2geq 1})) intersecting the surface {x = 0} under an additive control supported in an open subset ({omega=omega_1times Omega_2}) of ({Omega}).