Sharp Time Decay and Scattering of Small Data Solutions to the Relativistic Vlasov-Maxwell System
Abstract
A multispecies, collisionless plasma is modeled by the relativistic Vlasov-Maxwell system. Assuming the plasma is globally neutral, we show that solutions can be constructed with arbitrarily fast, polynomial rates of decay, depending upon the cancellation properties of the limiting spatial averages, as well as the masses and charges of the particles. In doing so, we establish a countably infinite number of asymptotic profiles for the charge and current density, electric and magnetic fields, and their derivatives, each of which is necessarily realized by a sufficiently smooth solution. Our approach relies upon a refined field representation that features self-similar behavior away from the boundary of the light cone. In each case we establish a linear scattering result in L∞ for every particle distribution function, namely we show that they converge as t → ∞ along the transported spatial characteristics at increasingly faster rates. In the case that charge cancellation does not occur, our methods can be further extended to demonstrate polyhomogeneous expansions with logarithmic corrections.
Related
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BibTeX
@misc{mattingly2026sharp,
title = {{Sharp Time Decay and Scattering of Small Data Solutions to the Relativistic Vlasov-Maxwell System}},
author = {Grace Mattingly and Stephen Pankavich and Jonathan Ben-Artzi},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.29013},
eprint = {2609.29013},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.29013},
}
RIS
TY - UNPB
TI - Sharp Time Decay and Scattering of Small Data Solutions to the Relativistic Vlasov-Maxwell System
AU - Grace Mattingly
AU - Stephen Pankavich
AU - Jonathan Ben-Artzi
PY - 2026
DA - 2026/09/24
PB - arXiv
DO - 10.48550/arxiv.2609.29013
UR - https://arxiv.org/abs/2609.29013
AB - A multispecies, collisionless plasma is modeled by the relativistic Vlasov-Maxwell system. Assuming the plasma is globally neutral, we show that solutions can be constructed with arbitrarily fast, polynomial rates of decay, depending upon the cancellation properties of the limiting spatial averages, as well as the masses and charges of the particles. In doing so, we establish a countably infinite number of asymptotic profiles for the charge and current density, electric and magnetic fields, and their derivatives, each of which is necessarily realized by a sufficiently smooth solution. Our approach relies upon a refined field representation that features self-similar behavior away from the boundary of the light cone. In each case we establish a linear scattering result in L^∞ for every particle distribution function, namely we show that they converge as t → ∞ along the transported spatial characteristics at increasingly faster rates. In the case that charge cancellation does not occur, our methods can be further extended to demonstrate polyhomogeneous expansions with logarithmic corrections.
ER -