AI 中文总结
本文针对具多项式增长势的McKean-Vlasov扩散，通过熵耗散方法证明了[Mal01]未证结果，推广至非混沌非交换初条件，突破Lipschitz设定并获时间一致混沌传播生成界。
AI 中文摘要
我们研究一类具有多项式增长势的McKean-Vlasov方程的时间一致混沌传播与生成问题。采用基于时间一致对数 Sobolev 不等式的熵耗散方法，我们推导了依赖于势的正则性与初始条件假设的时间一致界。由此，我们不仅证明了[Mal01]中已陈述但未证明的结果，还将其推广至非混沌、非交换的初始条件，突破了经典的 Lipschitz 设定，代价是收敛速率出现对数损失。
英文摘要
We study time-uniform propagation and generation of chaos for a class of McKean-Vlasov equations with polynomial growth potentials. Using an entropy dissipation method based on time-uniform logarithmic Sobolev inequalities, we derive uniform-in-time bounds depending on the regularity of the potentials and the assumptions on the initial conditions. We thereby not only establish a result stated but unproven in [Mal01], but also extend it to non-chaotic and non-exchangeable initial conditions, moving beyond the classical Lipschitz setting at the expense of a logarithmic loss in the convergence rate.
