相对论 Nordström-Vlasov 方程解的正则性

数学物理学报 ›› 2023, Vol. 43 ›› Issue (3): 743-753.

相对论 Nordström-Vlasov 方程解的正则性

陈蕊娟¹(),何映羲²(),肖梅霞^1,^*()

¹武汉纺织大学数理科学学院, 非线性研究中心武汉 430200
²Business School, University of Essex Wivenhoe Park, Colchester CO4 3SQ

收稿日期:2022-01-26 修回日期:2022-10-28 出版日期:2023-06-26 发布日期:2023-06-01
通讯作者: 肖梅霞 E-mail:ruijuanchen@hust.edu.cn;yh20602@essex.ac.uk;xiao_meixia@163.com
作者简介:陈蕊娟, E-mail: ruijuanchen@hust.edu.cn;|何映羲,E-mail: yh20602@essex.ac.uk
基金资助:
国家自然科学基金(12001406);湖北省教育厅科学技术研究项目(B2021095)

Regularity of the Solutions to the Nordström-Vlasov System

Chen Ruijuan¹(),He YingXi²(),Xiao Meixia^1,^*()

¹Research Center of Nonlinear Science, School of Mathematical and Physical Sciences, Wuhan Textile University, Wuhan 430200
²Essex business school, University of essex Wivenhoe Park, Colchester CO4 3SQ

Received:2022-01-26 Revised:2022-10-28 Online:2023-06-26 Published:2023-06-01
Contact: Meixia Xiao E-mail:ruijuanchen@hust.edu.cn;yh20602@essex.ac.uk;xiao_meixia@163.com
Supported by:
NSFC(12001406);Science and Technology Research Project of Education Department of Hubei Province(B2021095)

摘要/Abstract

摘要：

该文研究的是相对论 Nordström-Vlasov 方程整体解的正则性问题. 这个动力学模型是经典的 asov-Poisson 方程在引力情况下的相对论推广, 描述了无碰撞粒子通过自身诱导的向量引力场之间的相互作用. 通过傅里叶分析和低速粒子的光滑效应, 该文得到了一个弱解正则性结果.

关键词: Nordström-Vlasov 方程, 正则性, 傅里叶分析

Abstract:

In this paper, we investigate the Nordström-Vlasov system in the whole space. The kinetic model is a relativistic generalization of the classical Vlasov-Poisson system in the gravitational case and describes the ensemble motion of collisionless particles interacting by means of a self-consistent scalar gravitational field. With the Fourier analysis and the smoothing effect of low velocity particles, we get a regularity of weak solutions for the field.

Key words: Nordström-Vlasov system, Regularity, Fourier analysis

中图分类号:

O175.2

陈蕊娟, 何映羲, 肖梅霞. 相对论 Nordström-Vlasov 方程解的正则性[J]. 数学物理学报, 2023, 43(3): 743-753.

Chen Ruijuan, He YingXi, Xiao Meixia. Regularity of the Solutions to the Nordström-Vlasov System[J]. Acta mathematica scientia,Series A, 2023, 43(3): 743-753.

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