Global-in-time mean-field convergence for singular Riesz-type diffusive flows

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2021-08-23 DOI:10.1214/22-aap1833

M. Rosenzweig, S. Serfaty

引用次数: 22

Abstract

We consider the mean-field limit of systems of particles with singular interactions of the type $-\log|x|$ or $|x|^{-s}$, with $00$, the convergence is global in time, and it is the first such result valid for both conservative and gradient flows in a singular setting on $\mathbb{R}^d$. The proof relies on an adaptation of an argument of Carlen-Loss to show a decay rate of the solution to the limiting equation, and on an improvement of the modulated-energy method developed in arXiv:1508.03377, arXiv:1803.08345, arXiv:2107.02592 making it so that all prefactors in the time derivative of the modulated energy are controlled by a decaying bound on the limiting solution.

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奇异riesz型扩散流的全局实时平均场收敛性

考虑了具有$-\log|x|$或$|x|^{-s}$奇异相互作用的粒子系统的平均场极限，在$00$下，收敛在时间上是全局的，这是第一个在$\mathbb{R}^d$上的奇异设置下保守流和梯度流都有效的结果。该证明依赖于对Carlen-Loss的一个论证的改编，以显示极限方程解的衰减率，并依赖于对arXiv:1508.03377, arXiv:1803.08345, arXiv:2107.02592中提出的调制能量方法的改进，使得调制能量的时间导数中的所有前因子都由极限解的衰减界控制。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.