The Mean-Field Limit for a Regularized Vlasov-Maxwell Dynamics
The Mean-Field Limit for a Regularized Vlasov-Maxwell Dynamics
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正则化 Vlasov-Maxwell 动力学的平均场极限
DOI：
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发表时间：
2011
影响因子：
2.4
通讯作者：
F. Golse
中科院分区：
文献类型：
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作者：
F. Golse
本工作建立了一个N粒子系统的平均场极限的相对论性弗拉索夫-麦克斯韦系统的正则化的变种，以下的工作Braun-Hepp [Commun Math Phys 56：101-113，1977]和Dobrushin [Func Anal Appl 13：115-123，1979]的弗拉索夫-泊松系统。分析这个系统的主要成分是（a）根据动量变量中电磁势的分布的麦克斯韦方程的动力学公式，（B）一个正则化过程，其中总能量的类似物-即粒子的动能加上电磁场的能量-是守恒的，以及（c）Dobrushin对Monge的稳定性估计的类似物-适用于延迟势的正则化Vlasov-Poisson动力学的两个解之间的Kantorovich-Rubinstein距离。
The present work establishes the mean-field limit of a N-particle system towards a regularized variant of the relativistic Vlasov-Maxwell system, following the work of Braun-Hepp [Commun Math Phys 56:101–113, 1977] and Dobrushin [Func Anal Appl 13:115–123, 1979] for the Vlasov-Poisson system. The main ingredients in the analysis of this system are (a) a kinetic formulation of the Maxwell equations in terms of a distribution of electromagnetic potential in the momentum variable, (b) a regularization procedure for which an analogue of the total energy—i.e. the kinetic energy of the particles plus the energy of the electromagnetic field—is conserved and (c) an analogue of Dobrushin’s stability estimate for the Monge-Kantorovich-Rubinstein distance between two solutions of the regularized Vlasov-Poisson dynamics adapted to retarded potentials.