Mixing Estimates for Passive Scalar Transport by BV Vector Fields

2025/04/03 by Huysmans, Lucas, Said, Ayman Rimah · 2 citations
#35Q35 #76F25 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2504.03023

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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• Introduction to the theory of mixing for incompressible flows
• A priori error estimates for the θ-method for the flow of nonsmooth velocity fields

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