具有镜面反射边界条件的动力学Fokker-Planck和Landau方程

IF 1 4区数学 Q1 MATHEMATICS

Kinetic and Related Models Pub Date : 2021-11-18 DOI:10.3934/krm.2022003

Hongjie Dong, Yan Guo, Timur Yastrzhembskiy

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引用次数: 7

摘要

We establish existence of finite energy weak solutions to the kinetic Fokker-Planck equation and the linear Landau equation near Maxwellian, in the presence of specular reflection boundary condition for general domains. Moreover, by using a method of reflection and the \begin{document}$ S_p $\end{document} estimate of [7], we prove regularity in the kinetic Sobolev spaces \begin{document}$ S_p $\end{document} and anisotropic Hölder spaces for such weak solutions. Such \begin{document}$ S_p $\end{document} regularity leads to the uniqueness of weak solutions.

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Kinetic Fokker-Planck and Landau equations with specular reflection boundary condition

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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.