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The Vlasov-Maxwell point charge system : study of the spherically symmetric case

  • Emile Breton
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Abstract

We consider the Vlasov-Maxwell system with a repulsive point charge. Under a spherical symmetry condition, this reduces to the relativistic Vlasov-Poisson system with a point charge. For this system, the linear characteristics solve the equations of motion for the relativistic Kepler problem. We define action-angle variables for the linearized equation, and then study the nonlinear system in these coordinates. Within this framework, we prove global existence of classical solutions for small initial data and establish their modified scattering behavior. The proof makes use of the ideas developed in the non-relativistic case.

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Cite

BibTeXRIS
BibTeX
@misc{breton2026vlasovmaxwell,
  title = {{The Vlasov-Maxwell point charge system : study of the spherically symmetric case}},
  author = {Emile Breton},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.00973},
  eprint = {2609.00973},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.00973},
}
RIS
TY  - UNPB
TI  - The Vlasov-Maxwell point charge system : study of the spherically symmetric case
AU  - Emile Breton
PY  - 2026
DA  - 2026/09/01
PB  - arXiv
DO  - 10.48550/arxiv.2609.00973
UR  - https://arxiv.org/abs/2609.00973
AB  - We consider the Vlasov-Maxwell system with a repulsive point charge. Under a spherical symmetry condition, this reduces to the relativistic Vlasov-Poisson system with a point charge. For this system, the linear characteristics solve the equations of motion for the relativistic Kepler problem. We define action-angle variables for the linearized equation, and then study the nonlinear system in these coordinates. Within this framework, we prove global existence of classical solutions for small initial data and establish their modified scattering behavior. The proof makes use of the ideas developed in the non-relativistic case.
ER  -