• Corpus ID: 226965576

# Mean-field limit and quantitative estimates with singular attractive kernels

@article{Bresch2020MeanfieldLA,
title={Mean-field limit and quantitative estimates with singular attractive kernels},
author={Didier Bresch and Pierre-Emmanuel Jabin and Zhenfu Wang},
journal={arXiv: Analysis of PDEs},
year={2020}
}
• Published 13 November 2020
• Mathematics
• arXiv: Analysis of PDEs
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…
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We propose a new approach to obtain quantitative convergence of moderately interacting particle systems to solutions of nonlinear Fokker-Planck equations with singular kernels. Our result only
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This is the document corresponding to the talk the first author gave at IH{E}S for the Laurent Schwartz seminar on November 19, 2019. It concerns our recent introduction of a modulated free energy in
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The Keller-Segel system describes the collective motion of cells which are attracted by a chemical substance and are able to emit it. In its simplest form it is a conservative drift-diffusion
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