MEAN FIELD LIMIT AND QUANTITATIVE ESTIMATES WITH SINGULAR ATTRACTIVE KERNELS

被引：16

作者：

Bresch, Didier ^{[1
]}

Jabin, Pierre-Emmanuel ^{[2
,3
]}

Wang, Zhenfu ^{[4
]}

机构：

[1] Univ Savoie Mt Blanc, Lab Math, CNRS UMR 5127, Le Bourget Du Lac, France

[2] Penn State Univ, Dept Math, State Coll, PA USA

[3] Penn State Univ, Huck Inst, State Coll, PA USA

[4] Peking Univ, Beijing Int Ctr Math Res, Beijing, Peoples R China

来源：

DUKE MATHEMATICAL JOURNAL | 2023年 / 172卷 / 13期

基金：

美国国家科学基金会;

关键词：

STOCHASTIC PARTICLE APPROXIMATION; PATLAK-KELLER-SEGEL; QUASI-NEUTRAL LIMIT; NAVIER-STOKES; PROPAGATION; CHAOS; EQUATIONS; EXISTENCE; SYSTEM; MODEL;

D O I：

10.1215/00127094-2022-0088

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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 Seminaire Laurent Schwartz, we provide the full proof of results announced by the authors in 2019.

引用

页码：2591 / 2641

页数：51

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