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arXiv · 2107.02592

Mean-field limits of Riesz-type singular flows

Quoc Hung Nguyen·Matthew Rosenzweig·Sylvia Serfaty
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Abstract

We provide a proof of mean-field convergence of first-order dissipative or conservative dynamics of particles with Riesz-type singular interaction (the model interaction is an inverse power $s$ of the distance for any $0<s<d$) when assuming a certain regularity of the solutions to the limiting evolution equations. It relies on a modulated-energy approach, as introduced in previous works where it was restricted to the Coulomb and super-Coulombic cases. The method is also capable of incorporating multiplicative noise of transport type into the dynamics. It relies in extending functional inequalities of arXiv:1803.08345, arXiv:2011.12180, arXiv:2003.11704 to more general interactions, via a new, robust proof that exploits a certain commutator structure.

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Quoc Hung Nguyen, Matthew Rosenzweig, Sylvia Serfaty. 2021-07-06. Mean-field limits of Riesz-type singular flows. https://doi.org/10.15781/nvv7-jy87

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