动力学Fokker-Planck方程的时间平均值

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2021-06-24 DOI:10.3934/krm.2022037

G. Brigati

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引用次数: 8

摘要

我们考虑环面上具有麦克斯韦局部平衡或肥尾局部平衡的动力学Fokker-Planck(或Vlasov-Fokker-Planck)方程。S. Armstrong和j . c . c .最近取得了基于弱规范的结果。在麦克斯韦局部均衡的情况下。利用改进的Poincar\'e和lions型不等式，我们开发了一种估算解的范数时间平均衰减率的显式和建设性方法，该方法涵盖了对应于亚指数、指数和超指数(包括麦克斯韦)局部平衡的各种区域。因此，我们还得到了低矫顽力估计，并将其与其他技术获得的类似结果进行了比较。

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Time averages for kinetic Fokker-Planck equations

We consider kinetic Fokker-Planck (or Vlasov-Fokker-Planck) equations on the torus with Maxwellian or fat tail local equilibria. Results based on weak norms have recently been achieved by S. Armstrong and J.-C. Mourrat in case of Maxwellian local equilibria. Using adapted Poincar\'e and Lions-type inequalities, we develop an explicit and constructive method for estimating the decay rate of time averages of norms of the solutions, which covers various regimes corresponding to subexponential, exponential and superexponential (including Maxwellian) local equilibria. As a consequence, we also derive hypocoercivity estimates, which are compared to similar results obtained by other techniques.

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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.