Long-Time Dynamics of the 3D Vlasov-Maxwell System with Boundaries
Abstract
We construct global-in-time classical solutions to the nonlinear Vlasov-Maxwell system in a three-dimensional half-space beyond the vacuum scattering regime. Our approach combines the construction of stationary solutions to the associated boundary-value problem with a proof of their asymptotic dynamical stability in under small perturbations, providing a new framework for understanding long-time wave-particle interactions in the presence of boundaries and interacting magnetic fields. To the best of our knowledge, this work presents the first construction of asymptotically stable non-vacuum steady states under general perturbations in the full three-dimensional nonlinear Vlasov-Maxwell system.
Keywords
Cite
@article{arxiv.2509.11064,
title = {Long-Time Dynamics of the 3D Vlasov-Maxwell System with Boundaries},
author = {Jin Woo Jang and Chanwoo Kim},
journal= {arXiv preprint arXiv:2509.11064},
year = {2025}
}
Comments
This is the full detailed version containing all proofs and additional technical details. It is posted (arXiv:2509.11064v2) for the convenience of readers and is not intended for separate publication. The published or submitted article corresponds to a shorter version of this work. The full version also includes a vacuum asymptotic stability result (Section 10). 110 pages