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arXiv · 2011.08022

Mean-field limit and quantitative estimates with singular attractive kernels

Didier Bresch·Pierre-Emmanuel Jabin·Zhenfu Wang
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Abstract

This paper proves the mean field limit and quantitative estimates for many-particle systems with singular attractive interactions between particles. As an important example, a full rigorous derivation (with quantitative estimates) of the Patlak-Keller-Segel model in optimal subcritical regimes is obtained for the first time. To give an answer to this longstanding problem, we take advantage of a new modulated free energy and we prove some precise large deviation estimates encoding the competition between diffusion and attraction. Combined with the range of repulsive kernels, already treated in the s{\'e}minaire Laurent Schwartz proceeding [https://slsedp.centre-mersenne.org/journals/SLSEDP/ ], we provide the full proof of results announced by the authors in [C. R. Acad. Sciences Section Maths (2019)].

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Didier Bresch, Pierre-Emmanuel Jabin, Zhenfu Wang. 2020-11-16. Mean-field limit and quantitative estimates with singular attractive kernels. https://arxiv.org/abs/2011.08022

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