A Moser-Type Construction for the Liouville Equation
Optimization and Control
2026-03-24 v1
Abstract
We present a novel extension of Moser's volume form lemma to the kinetic Liouville equation. In particular, we show that two smooth, positive phase-space densities and can be connected in unit time by the Liouville equation if and only if a natural compatibility condition on velocity marginals is satisfied. Under this condition, an explicit family of force fields is constructed via a weighted elliptic problem in the velocity variable. Results of numerical experiments are presented to validate the theoretical framework.
Cite
@article{arxiv.2603.21850,
title = {A Moser-Type Construction for the Liouville Equation},
author = {Alfio Borzì and Marco Caponigro and Arianna Vicari},
journal= {arXiv preprint arXiv:2603.21850},
year = {2026}
}