关于具有镜面反射的半空间中的Lanford定理

IF 16.4 1区 化学 Q1 CHEMISTRY, MULTIDISCIPLINARY Accounts of Chemical Research Pub Date : 2021-02-10 DOI:10.3934/krm.2022028
Th'eophile Dolmaire
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引用次数: 3

摘要

本文给出了半空间中玻尔兹曼方程的一个严格推导。我们在这个领域给出了Lanford定理的一个类比,在镜面反射边界条件下,说明了N个硬球系统的密度函数的第一个边缘的低密度极限收敛于与单粒子密度函数初始状态对应的初始数据相关的Boltzmann方程的解。这项工作的原始贡献主要包括两个方面:碰撞算子和BBGKY层次结构在强意义上求解的功能空间的严格定义;以及Gallagher、Saint- Raymond和Texier对半空间情况下记忆控制的适应,这是获得兰福德定理定量版本的关键一步。
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About Lanford's theorem in the half-space with specular reflection
The present article proposes a rigorous derivation of the Boltzmann equation in the half-space. We show an analog of the Lanford's theorem in this domain, with specular reflection boundary condition, stating the convergence in the low density limit of the first marginal of the density function of a system of N hard spheres towards the solution of the Boltzmann equation associated to the initial data corresponding to the initial state of the one-particle-density function. The original contributions of this work consist in two main points: the rigorous definition of the collision operator and of the functional space in which the BBGKY hierarchy is solved in a strong sense; and the adaptation to the case of the half-space of the control of the recollisions performed by Gallagher, Saint- Raymond and Texier, which is a crucial step to obtain a quantitative version of the Lanford's theorem.
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来源期刊
Accounts of Chemical Research
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.
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