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Chen, Li; Li, Xin; Pickl, Peter and Yin, Qitao (2020): Combined mean field limit and non-relativistic limit of Vlasov-Maxwell particle system to Vlasov-Poisson system. In: Journal of Mathematical Physics, Vol. 61, No. 6, 061903

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In this paper, we consider the mean field limit and non-relativistic limit of the relativistic Vlasov-Maxwell particle system to the Vlasov-Poisson equation. With the relativistic Vlasov-Maxwell particle system being a starting point, we carry out the estimates (with respect toNandc) between the characteristic equation of both the Vlasov-Maxwell particle model and the Vlasov-Poisson equation, where the probabilistic method is exploited. In the last step, we take both a largeNlimit and a non-relativistic limit (meaningctending to infinity) to close the argument. Deriving such a mean-field limit for interactions with Coulomb singularity is a difficult task;therefore, we introduce anN-dependent 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 Vlasov-Maxwell in the non-relativistic setting.

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