Lyapunov exponents, entropy and mixing for DiPerna-Lions flows
Analysis of PDEs
2025-10-06 v1 Dynamical Systems
Abstract
The main goal of this work is to establish an asymptotic form of Bressan's mixing conjecture. To this end, we develop an ergodic-theoretic framework for incompressible DiPerna-Lions flows. Lyapunov exponents are defined via an Oseledets-type decomposition and related to metric entropy through a version of Ruelle's inequality in this low-regularity setting. These tools yield sharp bounds on asymptotic regularity propagation and mixing rates, leading to our main result.
Keywords
Cite
@article{arxiv.2510.02921,
title = {Lyapunov exponents, entropy and mixing for DiPerna-Lions flows},
author = {Elia Brué and Maria Colombo and Carl Johan Peter Johansson},
journal= {arXiv preprint arXiv:2510.02921},
year = {2025}
}
Comments
29 pages