Lower bound for the Boltzmann equation whose regularity grows tempered with time

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2021-01-01 DOI:10.3934/krm.2021020

Lingbing He, Jie Ji, Ling-Xuan Shao

引用次数: 0

Abstract

As a first step towards the general global-in-time stability for the Boltzmann equation with soft potentials, in the present work, we prove the quantitative lower bounds for the equation under the following two assumptions, which stem from the available energy estimates, i.e. (ⅰ). the hydrodynamic quantities (local mass, local energy, and local entropy density) are bounded (from below or from above) uniformly in time, (ⅱ). the Sobolev regularity for the solution grows tempered with time.

查看原文本刊更多论文

玻尔兹曼方程的下界，其规律性随时间而变弱

作为研究具有软势的玻尔兹曼方程的一般全局时间稳定性的第一步，在本文中，我们在以下两个假设下证明了该方程的定量下界，这两个假设源于可用的能量估计，即(ⅰ)。水动力量(局部质量、局部能量和局部熵密度)在时间上均匀地(从下或从上)有界，(ⅱ)。解的Sobolev规律性随着时间的推移而变弱。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

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.