On the commutativity of flows of rough vector fields

2020/11/16 by Colombo, Maria, Tione, Riccardo · 2 citations
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2011.08133

Abstract

In the class of Sobolev vector fields in ℝⁿ of bounded divergence, for which the theory of DiPerna and Lions provides a well defined notion of flow, we characterize the vector fields whose flow commute in terms of the Lie bracket and of a regularity condition on the flows themselves. This extends a classical result of Frobenius in the smooth setting.

Cited by

• A general Frobenius' Theorem via the Transport of Currents
• Chow and Rashevskii meet Sobolev

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