Long time behavior of the Vlasov-Maxwell-Fokker-Planck system with a strong external magnetic field
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866915448668291072 |
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| author | Vu, Anh-Tuan |
| author_facet | Vu, Anh-Tuan |
| contents | The subject matter of this paper concerns the magnetic confinement of plasma. We investigate the long time behavior of the Vlasov-Maxwell-Fokker-Planck system under the effect of a strong external magnetic field. We first formally derive an asymptotically reduced model. In three space dimensions, a constraint occurs along the parallel direction to the magnetic field. To eliminate the corresponding Lagrange multiplier, we then study the Vlasov-Maxwell-Fokker-Planck system in two spatial dimensions and three velocity dimensions. In this setting, we show that the obtained asymptotic model defines a well-posed dynamical system, and we provide a rigorous mathematical justification of the formally derived system. Our proofs rely on the modulated energy method. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_12231 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Long time behavior of the Vlasov-Maxwell-Fokker-Planck system with a strong external magnetic field Vu, Anh-Tuan Analysis of PDEs 35Q75, 78A35, 82D10 The subject matter of this paper concerns the magnetic confinement of plasma. We investigate the long time behavior of the Vlasov-Maxwell-Fokker-Planck system under the effect of a strong external magnetic field. We first formally derive an asymptotically reduced model. In three space dimensions, a constraint occurs along the parallel direction to the magnetic field. To eliminate the corresponding Lagrange multiplier, we then study the Vlasov-Maxwell-Fokker-Planck system in two spatial dimensions and three velocity dimensions. In this setting, we show that the obtained asymptotic model defines a well-posed dynamical system, and we provide a rigorous mathematical justification of the formally derived system. Our proofs rely on the modulated energy method. |
| title | Long time behavior of the Vlasov-Maxwell-Fokker-Planck system with a strong external magnetic field |
| topic | Analysis of PDEs 35Q75, 78A35, 82D10 |
| url | https://arxiv.org/abs/2508.12231 |