Geodesic
Mean-field limits of Riesz-type singular flows
Ars Inveniendi Analytica (2022).

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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 $0$) 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.
Publié le :
DOI : 10.15781/nvv7-jy87 
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     author = {Quoc Hung Nguyen and Matthew Rosenzweig and Sylvia Serfaty},
     title = {Mean-field limits of {Riesz-type} singular flows},
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     year = {2022},
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Quoc Hung Nguyen; Matthew Rosenzweig; Sylvia Serfaty. Mean-field limits of Riesz-type singular flows. Ars Inveniendi Analytica (2022). doi : 10.15781/nvv7-jy87. http://geodesic.mathdoc.fr/articles/10.15781/nvv7-jy87/

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