Null-controllability of non-autonomous Ornstein-Uhlenbeck equations

We study the null-controllability of parabolic equations associated to non-autonomous Ornstein-Uhlenbeck operators. When a Kalman type condition holds for some positive time T>0, these parabolic equations are shown to enjoy a Gevrey regularizing effect at time T>0. Thanks to this regularizing effect, we prove by adapting the Lebeau-Robbiano method that these parabolic equations are null-controllable in time T>0 from control regions, for which null-controllability is classically known to hold in the case of the heat equation.