Regularity estimates for the flow of BV autonomous divergence-free planar vector fields

Abstract: We consider the appropriate notion of flow $X$ associated to a bounded divergence-free vector field $b$ with bounded variation in the plane. 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 $1/t$ as $t\to \infty$. This is a joint work with Paolo Bonicatto.

analysis of PDEs

Audience: researchers in the topic

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