Long-Time Dynamics of the 3D Vlasov-Maxwell System with Boundaries
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866911191675174912 |
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| author | Jang, Jin Woo Kim, Chanwoo |
| author_facet | Jang, Jin Woo Kim, Chanwoo |
| contents | 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 $L^\infty$ 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_11064 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Long-Time Dynamics of the 3D Vlasov-Maxwell System with Boundaries Jang, Jin Woo Kim, Chanwoo Analysis of PDEs 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 $L^\infty$ 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. |
| title | Long-Time Dynamics of the 3D Vlasov-Maxwell System with Boundaries |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2509.11064 |