调制Gibbs测度与三维Vlasov–Poisson–Fokker–Planck方程的均值场极限
Modulated Gibbs Measure and Mean-Field Limit for 3D Vlasov--Poisson--Fokker--Planck Equations
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中文总结 AI 辅助
本文通过引入调制Gibbs测度并结合加权BBGKY估计，首次在短时间区间上为三维VPFP方程建立了无截断的均值场极限与混沌传播。
中文摘要 AI 辅助
我们为具有奇异排斥相互作用的随机牛顿系统在通常的张量化初始数据下引入了一种调制Gibbs测度。利用Wang–Zhao的关于配分函数的均匀N估计，我们证明了调制Gibbs测度与其张量化参考在归一化相对熵意义下是O(N^{-1})接近的。随后，一个稳定性论证将混沌传播从调制Gibbs测度转移到张量化数据及其他初始律，且保持相同的熵尺度。结合Bresch–Jabin–Soler的加权BBGKY估计，这首次在N无关的短时间区间上为三维Vlasov–Poisson–Fokker–Planck (VPFP)方程提供了无截断的均值场极限和混沌传播。
英文摘要
We introduce a modulated Gibbs measure for the usual tensorized initial data for stochastic Newton's systems with singular repulsive interactions. Using the uniform-in-$N$ partition-function estimates of Wang--Zhao \cite{wang2026uniform}, we show that the modulated Gibbs measure and its tensorized reference are $O(N^{-1})$-close in normalized relative entropy. A stability argument then transfers propagation of chaos from modulated Gibbs measures to tensorized data and other initial laws at the same entropy scale. Combined with the weighted BBGKY estimates of Bresch--Jabin--Soler \cite{bresch2025new}, this yields the first cutoff-free mean-field limit and propagation of chaos for the three-dimensional Vlasov--Poisson--Fokker--Planck (VPFP) equation on an $N$-independent short-time interval.
发表机构
- School of Mathematical Sciences, Peking University（北京大学数学科学学院）
- Beijing International Center for Mathematical Research, Peking University（北京大学北京国际数学研究中心）
机构由 AI 辅助整理，请以论文原文为准。
