Chen, Li; Li, Xin; Pickl, Peter; Yin, Qitao
(2020):
Combined mean field limit and nonrelativistic limit of VlasovMaxwell particle system to VlasovPoisson system.
In: Journal of Mathematical Physics, Vol. 61, No. 6, 061903

Full text not available from 'Open Access LMU'.
Abstract
In this paper, we consider the mean field limit and nonrelativistic limit of the relativistic VlasovMaxwell particle system to the VlasovPoisson equation. With the relativistic VlasovMaxwell particle system being a starting point, we carry out the estimates (with respect toNandc) between the characteristic equation of both the VlasovMaxwell particle model and the VlasovPoisson equation, where the probabilistic method is exploited. In the last step, we take both a largeNlimit and a nonrelativistic limit (meaningctending to infinity) to close the argument. Deriving such a meanfield limit for interactions with Coulomb singularity is a difficult task;therefore, we introduce anNdependent mollifier to smoothen the interactions. Note that the length scale of our mollifier isN(alpha)for an alpha that can be chosen arbitrarily close to but smaller than 1/3, which improves previous results in the literature on deriving VlasovMaxwell in the nonrelativistic setting.