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The uniform-in-time electrostatic limit of the linearised Vlasov-Maxwell system: the Poisson equilibrium

  • Marnie Smith
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Abstract

The Vlasov-Maxwell system with Newtonian particle transport is linearised about the Poisson equilibrium on ℝ3, with the speed of light c treated as a large parameter. For uniformly controlled initial data, with transverse fields that may remain of order one, the difference between the Vlasov-Maxwell perturbation and its linearised Vlasov-Poisson counterpart is bounded uniformly in time by their initial discrepancy plus a term of order c−1. The same estimate holds for their scattering states, and the rate in c is sharp. The longitudinal dynamics are governed by the same Volterra equation as in linearised Vlasov-Poisson and undergo Landau damping. The transverse fields exhibit Klein-Gordon-type dispersion, and control of their accumulated effect along free transport yields the uniform comparison.

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Cite

BibTeXRIS
BibTeX
@misc{smith2026uniformintime,
  title = {{The uniform-in-time electrostatic limit of the linearised Vlasov-Maxwell system: the Poisson equilibrium}},
  author = {Marnie Smith},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.23908},
  eprint = {2609.23908},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.23908},
}
RIS
TY  - UNPB
TI  - The uniform-in-time electrostatic limit of the linearised Vlasov-Maxwell system: the Poisson equilibrium
AU  - Marnie Smith
PY  - 2026
DA  - 2026/09/20
PB  - arXiv
DO  - 10.48550/arxiv.2609.23908
UR  - https://arxiv.org/abs/2609.23908
AB  - The Vlasov-Maxwell system with Newtonian particle transport is linearised about the Poisson equilibrium on ℝ^3, with the speed of light c treated as a large parameter. For uniformly controlled initial data, with transverse fields that may remain of order one, the difference between the Vlasov-Maxwell perturbation and its linearised Vlasov-Poisson counterpart is bounded uniformly in time by their initial discrepancy plus a term of order c^−1. The same estimate holds for their scattering states, and the rate in c is sharp. The longitudinal dynamics are governed by the same Volterra equation as in linearised Vlasov-Poisson and undergo Landau damping. The transverse fields exhibit Klein-Gordon-type dispersion, and control of their accumulated effect along free transport yields the uniform comparison.
ER  -