Calculus of Variations and Geometric Measure Theory

P. Bonicatto - E. Marconi

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 24 May 2021


Accepted Paper

Inserted: 8 oct 2019
Last Updated: 24 may 2021

Journal: Comm. in Partial Diff. Equations
Year: 2019


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 $t \to \infty$.