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arXiv · 1910.03277

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

Paolo Bonicatto·Elio Marconi
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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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Paolo Bonicatto, Elio Marconi. 2019-12-03. Regularity estimates for the flow of BV autonomous divergence free vector fields in $\mathbb{R}^2$. https://doi.org/10.1080/03605302.2021.1931883

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