标题： Vlasov方程和$N$体动力学 - 粒子动力学在我们对等离子体的理解中有多重要？ 显示英文标题

标题： Vlasov equation and $N$-body dynamics - How central is particle dynamics to our understanding of plasmas?

摘要： 建立库仑相互作用粒子的Vlasov方程的微观基础所遇到的困难被回顾，分别针对统计方法（BBGKY层次和相空间上的Liouville方程）和动力学方法（单个经验测度在单粒子$(\mathbf{r},\mathbf{v})$-空间上）。强调了粒子轨迹（特征）在分析偏微分Vlasov--Poisson系统中的作用。从多体动力学出发，简要描述了德拜屏蔽和集体行为的直接推导。 显示英文摘要

摘要： Difficulties in founding microscopically the Vlasov equation for Coulomb-interacting particles are recalled for both the statistical approach (BBGKY hierarchy and Liouville equation on phase space) and the dynamical approach (single empirical measure on one-particle $(\mathbf{r},\mathbf{v})$-space). The role of particle trajectories (characteristics) in the analysis of the partial differential Vlasov--Poisson system is stressed. Starting from many-body dynamics, a direct derivation of both Debye shielding and collective behaviour is sketched.