Mean-field limits for some Riesz interaction gradient flows

Mitia Duerinckx 1, 2, 3
2 MEPHYSTO - Quantitative methods for stochastic models in physics
Inria Lille - Nord Europe, ULB - Université Libre de Bruxelles [Bruxelles], LPP - Laboratoire Paul Painlevé - UMR 8524
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 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.
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  • HAL Id : hal-01252661, version 2
  • ARXIV : 1508.03377

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Mitia Duerinckx. Mean-field limits for some Riesz interaction gradient flows. SIAM Journal on Mathematical Analysis, Society for Industrial and Applied Mathematics, 2016, 48 (3), pp.2269-2300. ⟨hal-01252661v2⟩

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