论文标题
关于粗糙矢量场的流量的通勤
On the commutativity of flows of rough vector fields
论文作者
论文摘要
在$ \ mathbb {r}^n $中的Sobolev矢量字段中，diperna and Lions的理论提供了一个定义明确的流动概念，我们表征了矢量场，其流向以Lie Bracket和Flow Wellbs本身的规律性状态而流动通勤。这扩展了Frobenius在平滑环境中的经典结果。
In the class of Sobolev vector fields in $\mathbb{R}^n$ 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.
