A review of compactness methods for cross-diffusion systems seen as Wasserstein gradient flows
Analysis of PDEs
2026-04-03 v1
Abstract
A comprehensive methodology for establishing the existence of gradient flows for cross-diffusion systems with respect to suitable energies is proposed. The approach is based on the construction of piecewise-in-time constant approximations via the Jordan-Kinderlehrer-Otto scheme. Compactness of the approximate sequence is obtained using either the flow interchange technique or the five gradient inequality. These methods are illustrated for both parabolic and hyperbolic-parabolic Busenberg-Travis systems, as well as for several of their variants. This paper reviews the results from the literature and discusses additional properties.
Cite
@article{arxiv.2604.01819,
title = {A review of compactness methods for cross-diffusion systems seen as Wasserstein gradient flows},
author = {Mathias Dus and Ansgar Jüngel},
journal= {arXiv preprint arXiv:2604.01819},
year = {2026}
}