标题： 混合估计对于由$BV$向量场输运的被动标量的混合估计 显示英文标题

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

摘要： 我们证明了关于沿具有有界变差性的散度自由向量场的运输问题的定量混合估计。 通过发展一种量化Ambrosio正则化方案的框架，我们得出了针对一般 $BV$ 向量场的首个显式混合速率界限。 我们的分析表明，超指数（重复指数运算）出现在Ambrosio正则化的局部性质所导致的混合速率中。 显示英文摘要

摘要： 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.