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arXiv · 2511.18500

Classical limit of the relativistic Vlasov-Maxwell-Landau system

Chuqi Cao·Ling-Bing He·Yuanjie Lei·Qinghua Xiao
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Abstract

The physical essence of the non-relativistic limit, from the relativistic Vlasov-Maxwell-Landau system to the Vlasov-Poisson-Landau system, lies in the transition from finite-speed electromagnetic waves to instantaneous Coulomb interactions, and from relativistic to Newtonian particle dynamics. We rigorously justify this limit (mathematically corresponding to the light speed $c \to \infty$) in a periodic box via three key technical advances: establishing a uniform-in-$c$ coercivity estimate for the relativistic Landau collision operator, constructing a novel weighted energy functional to overcome the weakening dissipation of the electromagnetic field at large $c$, and proving a corresponding global well-posedness result.

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Chuqi Cao, Ling-Bing He, Yuanjie Lei, Qinghua Xiao. 2025-11-23. Classical limit of the relativistic Vlasov-Maxwell-Landau system. https://arxiv.org/abs/2511.18500

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