MEAN FIELD LIMIT AND QUANTITATIVE ESTIMATES WITH SINGULAR ATTRACTIVE KERNELS

Didier Bresch, Pierre Emmanuel Jabin, Zhenfu Wang

Research output: Contribution to journalArticlepeer-review

Abstract

We prove 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 long-standing problem, we take advantage of a new modulated free energy and prove some precise large deviation estimates encoding the competition between diffusion and attraction. Combined with the range of repulsive kernels, already treated in the proceedings of the Séminaire Laurent Schwartz, we provide the full proof of results announced by the authors in 2019.

Original languageEnglish (US)
Pages (from-to)2591-2641
Number of pages51
JournalDuke Mathematical Journal
Volume172
Issue number13
DOIs
StatePublished - 2023

All Science Journal Classification (ASJC) codes

  • General Mathematics

Cite this