Mean-field limits for some Riesz interaction gradient flows

Mitia Duerinckx (1, 2, 3)

1 ULB - Département de Mathématique [Bruxelles]
2 MEPHYSTO - Quantitative methods for stochastic models in physics
3 LJLL - Laboratoire Jacques-Louis Lions

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 the method introduced by Serfaty [24] in the context of the Ginzburg-Landau vortices, using regularity and stability properties of the limiting equation, we prove a mean-field limit result in dimensions 1 and 2 in cases for which this problem was still open.

Domaines: Equations aux dérivées partielles [math.AP]; Physique mathématique [math-ph]

Mitia Duerinckx. Mean-field limits for some Riesz interaction gradient flows. SIAM Journal on Mathematical Analysis, 2016, 48 (3), pp.2269-2300. ⟨hal-01252661v1⟩