Reducibility of Non-Resonant Transport Equation on $${\mathbb {T}}^d$$ T d with Unbounded Perturbations

Abstract

We prove reducibility of a transport equation on the $d$-dimensional torus $T^d$ with a time quasi-periodic unbounded perturbation. As far as we know this is the first example of a reducibility result for an equation in more than one dimensions with unbounded perturbations. Furthermore the unperturbed problem has eigenvalues whose differences are dense on the real axis.