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15 October 2020 Mean field limit for Coulomb-type flows
Sylvia Serfaty
Duke Math. J. 169(15): 2887-2935 (15 October 2020). DOI: 10.1215/00127094-2020-0019

Abstract

We establish the mean field convergence for systems of points evolving along the gradient flow of their interaction energy when the interaction is the Coulomb potential or a super-Coulombic Riesz potential, for the first time in arbitrary dimension. The proof is based on a modulated energy method using a Coulomb or Riesz distance, assumes that the solutions of the limiting equation are regular enough, and exploits a weak-strong stability property for them. The method can handle the addition of a regular interaction kernel and applies also to conservative and mixed flows. In the Appendix, it is also adapted to prove the mean field convergence of the solutions to Newton’s law with Coulomb or Riesz interaction in the monokinetic case to solutions of an Euler–Poisson type system.

Citation

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Sylvia Serfaty. "Mean field limit for Coulomb-type flows." Duke Math. J. 169 (15) 2887 - 2935, 15 October 2020. https://doi.org/10.1215/00127094-2020-0019

Information

Received: 2 April 2019; Revised: 9 February 2020; Published: 15 October 2020
First available in Project Euclid: 22 September 2020

MathSciNet: MR4158670
Digital Object Identifier: 10.1215/00127094-2020-0019

Subjects:
Primary: 35Q99
Secondary: 82C22

Rights: Copyright © 2020 Duke University Press

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Vol.169 • No. 15 • 15 October 2020
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