Geometric interpretation of the vanishing Lie Bracket for two-dimensional rough vector fields
Analysis of PDEs
2025-03-12 v2
Abstract
In this paper, we prove that if are continuous, Sobolev vector fields with bounded divergence on the real plane and , then their flows commute. In particular, we improve the previous result of Colombo-Tione (2021), where the authors require the additional assumption of the weak Lie differentiability on one of the two flows. We also discuss possible extensions to the setting.
Keywords
Cite
@article{arxiv.2406.02340,
title = {Geometric interpretation of the vanishing Lie Bracket for two-dimensional rough vector fields},
author = {Annalaura Rebucci and Martina Zizza},
journal= {arXiv preprint arXiv:2406.02340},
year = {2025}
}