Reducibility of Non-Resonant Transport Equation on Td with Unbounded Perturbations

We prove reducibility of a transport equation on the d-dimensional torus Td with a time quasiperiodic unbounded perturbation. As far as we know, this is one of the few reducibility results for an equation in more than one dimension with unbounded perturbations. Furthermore, the unperturbed problem has eigenvalues whose differences are dense on the real axis.