Mixing Estimates for Passive Scalar Transport by Vector Fields
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 vector fields. Our analysis reveals that tetration (repeated exponentiation) emerges in the mixing rate from the local nature of Ambrosio's regularisation.
27 pages