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arXiv · 2610.40422

Quantitative propagation of chaos on arbitrary finite time intervals for the three-dimensional repulsive Vlasov-Poisson-Fokker-Planck equation

Ning Jiang·Juntao Wu
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Abstract

We prove quantitative propagation of chaos in total variation for repulsive Vlasov--Riesz--Fokker--Planck (VRFP) equations on $\mathbb{T}^d$ and $\mathbb{R}^d$ with unregularized interaction potentials with singularity $|x|^{-s}$, $0 3$ gives convergence to the global classical solution on every finite time interval. The proof combines conditioning of the initial product law with weighted BBGKY estimates. A decomposition of the potential and a bounded modification of the far-field force yield weighted bounds growing geometrically in the marginal order on the prescribed interval. A centered second-moment estimate permits summation of the error hierarchy, and a synchronous coupling transfers the estimate to the original dynamics.

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Ning Jiang, Juntao Wu. 2026-10-29. Quantitative propagation of chaos on arbitrary finite time intervals for the three-dimensional repulsive Vlasov-Poisson-Fokker-Planck equation. https://arxiv.org/abs/2610.40422

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