On the mean field limit for Brownian particles with Coulomb interaction in 3D
© 2019 Author(s). In this paper, we consider the mean field limit of Brownian particles with Coulomb repulsion in 3D space using compactness. Using a symmetrization technique, we are able to control the singularity and prove that the limit measure almost surely is a weak solution to the limiting nonlinear Fokker-Planck equation. Moreover, by proving that the energy almost surely is bounded by the initial energy, we improve the regularity of the weak solutions. By a natural assumption, we also establish the weak-strong uniqueness principle, which is closely related to the propagation of chaos.
Volume / Issue
International Standard Serial Number (ISSN)
Digital Object Identifier (DOI)