小相对熵量子玻尔兹曼方程的全局存在性和大时间行为

IF 1 4区数学 Q1 MATHEMATICS

Kinetic and Related Models Pub Date : 2022-01-01 DOI:10.3934/krm.2022025

Yong Wang, C. Xiao, Yinghui Zhang

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引用次数: 0

摘要

In this paper, we study the global well-posedness of the non-relativistic quantum Boltzmann equation with initial data of small relative entropy. For a class of initial data which are allowed to have arbitrary bounded amplitude and even contain vacuum, we establish the global existence and uniqueness of the mild solutions to the quantum Boltzmann equation in the torus \begin{document}$ x\in\mathbb T^3 $\end{document}. The exponential time decay rate is also obtained in the \begin{document}$ L^{\infty}_{x, v} $\end{document}-norm.

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Global existence and large time behavior of the quantum Boltzmann equation with small relative entropy

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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.