Lyapunov exponents, entropy and mixing for DiPerna-Lions flows
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866909823283494912 |
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| author | Brué, Elia Colombo, Maria Johansson, Carl Johan Peter |
| author_facet | Brué, Elia Colombo, Maria Johansson, Carl Johan Peter |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_02921 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Lyapunov exponents, entropy and mixing for DiPerna-Lions flows Brué, Elia Colombo, Maria Johansson, Carl Johan Peter Analysis of PDEs Dynamical Systems 35Q35, 76F25, 37A35, 37A25 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. |
| title | Lyapunov exponents, entropy and mixing for DiPerna-Lions flows |
| topic | Analysis of PDEs Dynamical Systems 35Q35, 76F25, 37A35, 37A25 |
| url | https://arxiv.org/abs/2510.02921 |