Reducibility of non-resonant transport equation on $T^d$ with unbounded perturbations

TL;DR

This paper proves the reducibility of a multi-dimensional transport equation with unbounded, quasi-periodic perturbations, a novel result in higher dimensions with dense eigenvalue differences.

Contribution

It presents the first reducibility result for a multi-dimensional transport equation with unbounded perturbations, expanding the scope of such analyses.

Findings

First reducibility result in more than one dimension with unbounded perturbations

Eigenvalues of the unperturbed problem have dense differences on the real axis

Establishes a new approach for analyzing complex transport equations

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.