Mean-field limits for some Riesz interaction gradient flows
Analysis of PDEs
2016-07-06 v3 Mathematical Physics
math.MP
Abstract
This paper is concerned with the mean-field limit for the gradient flow evolution of particle systems with pairwise Riesz interactions, as the number of particles tends to infinity. Based on a modulated energy method, using regularity and stability properties of the limiting equation, as inspired by the work of Serfaty in the context of the Ginzburg-Landau vortices, we prove a mean-field limit result in dimensions 1 and 2 in cases for which this problem was still open.
Cite
@article{arxiv.1508.03377,
title = {Mean-field limits for some Riesz interaction gradient flows},
author = {Mitia Duerinckx},
journal= {arXiv preprint arXiv:1508.03377},
year = {2016}
}