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arXiv · 2504.03023

Mixing Estimates for Passive Scalar Transport by $BV$ Vector Fields

Lucas Huysmans·Ayman Rimah Said
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Abstract

We prove a quantitative mixing estimate for the Cauchy problem for transport along divergence-free vector fields with bounded variation. By developing a framework that quantifies Ambrosio's regularisation scheme, we derive the first explicit bounds on the mixing rate for general $BV$ vector fields. Our analysis reveals that tetration (repeated exponentiation) emerges in the mixing rate from the local nature of Ambrosio's regularisation.

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Lucas Huysmans, Ayman Rimah Said. 2025-04-03. Mixing Estimates for Passive Scalar Transport by $BV$ Vector Fields. https://arxiv.org/abs/2504.03023

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