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arXiv · 2609.23908

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 $\mathbb{R}^3$, 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.

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Marnie Smith. 2026-09-20. The uniform-in-time electrostatic limit of the linearised Vlasov-Maxwell system: the Poisson equilibrium. https://arxiv.org/abs/2609.23908

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