Mean-field limits for some Riesz interaction gradient flows

We investigate the mean-field limit for the gradient flow evolution of particle systems with pairwise singular interactions, as the number of particles tends to infinity. Based on a modulated energy method, we prove a new weak-strong stability principle for the limiting equation. This yields a quantitative proof of the mean-field result in dimensions 1 and 2 for a family of interactions for which this problem was still open.