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arXiv · 2510.02921

Lyapunov exponents, entropy and mixing for DiPerna-Lions flows

Elia Brué·Maria Colombo·Carl Johan Peter Johansson
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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.

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Elia Brué, Maria Colombo, Carl Johan Peter Johansson. 2025-10-03. Lyapunov exponents, entropy and mixing for DiPerna-Lions flows. https://arxiv.org/abs/2510.02921

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