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 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.

Mots clés: Mean-field limits; Riesz interactions; Fractional porous medium equation

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. ⟨10.1137/15M1042620⟩. ⟨hal-01252661v2⟩