Lyapunov exponents, entropy and mixing for DiPerna-Lions flows

2025/10/03 by Elia Brué, Brué, Elia, Maria Colombo +3
Mathematics · #Mathematical Dynamics and Fractals #Markov Chains and Monte Carlo Methods #Navier-Stokes equation solutions

paper · pdf · doi:10.48550/arxiv.2510.02921

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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• Rigorous enclosure of Lyapunov exponents of stochastic flows
• Introduction to the theory of mixing for incompressible flows
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