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Lyapunov exponents, entropy and mixing for DiPerna-Lions flows
Elia Bru\'e, Maria Colombo, Carl Johan Peter Johansson
https://arxiv.org/abs/2510.02921 https://

Lyapunov exponents, entropy and mixing for DiPerna-Lions flows
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.