相对论Nordstr?m-Vlasov方程解的正则性  

Regularity of the Solutions to the Nordström-Vlasov System

作　　者：陈蕊娟 何映羲 肖梅霞 Chen Ruijuan;He YingXi;Xiao Meixia(Research Center of Nonlinear Science,School of Mathematical and Physical Sciences,Wuhan Textile University,Wuhan 430200;Essex business school,University of essex Wivenhoe Park,Colchester CO43SQ)

机构地区：[1]武汉纺织大学数理科学学院,非线性研究中心,武汉4302002 [2]Business School,University of Essex Wivenhoe Park,Colchester CO43SQ

出　　处：《数学物理学报（A辑）》2023年第3期743-753,共11页Acta Mathematica Scientia

基　　金：国家自然科学基金(12001406);湖北省教育厅科学技术研究项目(B2021095)~~。

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Vlasov-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.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.

关 键 词：Nordström-Vlasov 方程 正则性 傅里叶分析 

分 类 号：O175.2[理学—数学]