English

Classical limit of the relativistic Vlasov-Maxwell-Landau system

Analysis of PDEs 2025-11-25 v1

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 cc \to \infty) in a periodic box via three key technical advances: establishing a uniform-in-cc 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 cc, and proving a corresponding global well-posedness result.

Keywords

Cite

@article{arxiv.2511.18500,
  title  = {Classical limit of the relativistic Vlasov-Maxwell-Landau system},
  author = {Chuqi Cao and Ling-Bing He and Yuanjie Lei and Qinghua Xiao},
  journal= {arXiv preprint arXiv:2511.18500},
  year   = {2025}
}