FLRW时空中无质量粒子的相对论BGK模型

IF 1 4区数学 Q1 MATHEMATICS

Kinetic and Related Models Pub Date : 2021-04-27 DOI:10.3934/krm.2021031

Byung-Hoon Hwang, Ho Lee, S. Yun

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引用次数: 5

摘要

本文讨论了由Anderson和Witting提出的关于Friedmann-Lemaȋtre-Robertson-Walker (FLRW)时空中无质量粒子的相对论性BGK模型的柯西问题。我们首先推导了FLRW时空中j ttner分布的显式形式，以及一组非线性关系，这些关系导致了麦克斯韦-玻尔兹曼粒子和玻色-爱因斯坦粒子的粒子数、动量和能量守恒定律。然后，我们找到了保证平衡系数满足非线性关系存在的充分条件，并证明了只要对初始步骤进行验证，就可以通过所有的归纳步骤来满足这个条件。利用这一观测，我们构造了FLRW时空中无质量粒子的Anderson-Witting型相对论性BGK模型的显式解。

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Relativistic BGK model for massless particles in the FLRW spacetime

In this paper, we address the Cauchy problem for the relativistic BGK model proposed by Anderson and Witting for massless particles in the Friedmann-Lemaȋtre-Robertson-Walker (FLRW) spacetime. We first derive the explicit form of the Jüttner distribution in the FLRW spacetime, together with a set of nonlinear relations that leads to the conservation laws of particle number, momentum, and energy for both Maxwell-Boltzmann particles and Bose-Einstein particles. Then, we find sufficient conditions that guarantee the existence of equilibrium coefficients satisfying the nonlinear relations and we show that the condition is satisfied through all the induction steps once it is verified for the initial step. Using this observation, we construct explicit solutions of the relativistic BGK model of Anderson-Witting type for massless particles in the FLRW spacetime.

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来源期刊

Kinetic and Related Models 数学-数学

CiteScore

2.10

自引率

10.00%

发文量

审稿时长

>12 weeks

期刊介绍： KRM publishes high quality papers of original research in the areas of kinetic equations spanning from mathematical theory to numerical analysis, simulations and modelling. It includes studies on models arising from physics, engineering, finance, biology, human and social sciences, together with their related fields such as fluid models, interacting particle systems and quantum systems. A more detailed indication of its scope is given by the subject interests of the members of the Board of Editors. Invited expository articles are also published from time to time.