On mean field limit for Brownian particles with Coulomb interaction in 3D
Analysis of PDEs
2020-01-08 v2 Mathematical Physics
math.MP
Probability
Abstract
In this paper, we consider the mean field limit of Brownian particles with Coulomb interaction in 3D space. In particular, using a symmetrization technique, we show that the limit measure almost surely is a weak solution to the limiting nonlinear Fokker-Planck equation. By proving that the energy almost surely is bounded by the initial energy, we improve the regularity of the weak solutions. Moreover, by a natural assumption, we establish the weak strong uniqueness principle, which is closely related to the propagation of chaos.
Keywords
Cite
@article{arxiv.1811.07797,
title = {On mean field limit for Brownian particles with Coulomb interaction in 3D},
author = {Lei Li and Jian-Guo Liu and Pu Yu},
journal= {arXiv preprint arXiv:1811.07797},
year = {2020}
}