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Mean-field limits for some Riesz interaction gradient flows

par Duerinckx, Mitia
Référence SIAM journal on mathematical analysis, 48, 3, page (2269-2300)
Publication Publié, 2016-12-01

Article révisé par les pairs

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Résumé :

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 in-finity. Based on the method introduced by Serfaty [Mean-Field Limits of the Gross-Pitaevskii and Parabolic Ginzburg-Landau equations, preprint, arXiv:1507.03821, 2015] 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.