# Regularity estimates for the flow of BV autonomous divergence free vector fields in $\mathbb{R}^2$

created by marconi on 08 Oct 2019
modified on 03 Dec 2019

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Submitted Paper

Inserted: 8 oct 2019
Last Updated: 3 dec 2019

Year: 2019

Abstract:

We consider the regular Lagrangian flow X associated to a bounded divergence-free vector field b with bounded variation. We prove a Lusin-Lipschitz regularity result for X and we show that the Lipschitz constant grows at most linearly in time. As a consequence we deduce that both geometric and analytical mixing have a lower bound of order $t^{-1}$ as $t \to \infty$.

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