Thermalization of a rarefied gas with total energy conservation: Existence, hypocoercivity, macroscopic limit

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2020-12-14 DOI:10.3934/krm.2022015

Gianluca Favre, M. Pirner, C. Schmeiser

引用次数: 3

Abstract

The thermalization of a gas towards a Maxwellian velocity distribution with the background temperature is described by a kinetic relaxation model. The sum of the kinetic energy of the gas and the thermal energy of the background are conserved, and the heat flow in the background is governed by the Fourier law.For the coupled nonlinear system of the kinetic and the heat equation, existence of solutions is proved on the one-dimensional torus. Spectral stability of the equilibrium is shown on the torus in arbitrary dimensions by hypocoercivity methods. The macroscopic limit towards a nonlinear cross-diffusion problem is carried out formally.

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总能量守恒的稀薄气体的热化:存在、低矫顽力、宏观极限

用动力学松弛模型描述了气体随背景温度向麦克斯韦速度分布的热化过程。气体的动能和背景的热能之和守恒，背景中的热流服从傅里叶定律。对于动力学方程和热方程耦合的非线性系统，在一维环面上证明了解的存在性。用准矫顽力方法证明了平衡态在环面任意维度上的谱稳定性。给出了非线性交叉扩散问题的宏观极限。

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.