The non-cutoff Vlasov-Poisson-Boltzmann system with weak collisions
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866911191881744384 |
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| author | Lei, Yuanjie Liu, Shuangqian Xiao, Qinghua Zhao, Huijiang |
| author_facet | Lei, Yuanjie Liu, Shuangqian Xiao, Qinghua Zhao, Huijiang |
| contents | We prove global existence of smooth solutions near Maxwellians for the non-cutoff Vlasov-Poisson-Boltzmann system in the weakly collisional regime. To address the weak dissipation of the non-cutoff linearized Boltzmann operator, we develop a refined velocity-weighted energy framework combined with vector-field techniques to control the transport term, nonlinear collisions, and the self-consistent electric field. This approach yields uniform-in-time bounds, captures enhanced dissipation of the solution, and establishes Landau damping for both the density and electric field, providing the first global-in-time result of this type for the non-cutoff Vlasov-Poisson-Boltzmann system. Our approach is inspired by the recent work of Chaturvedi-Luk-Nguyen ({\it J. Amer. Math. Soc.} {\bf 36} (2023), no. 4, 1103--1189.) |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_03835 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The non-cutoff Vlasov-Poisson-Boltzmann system with weak collisions Lei, Yuanjie Liu, Shuangqian Xiao, Qinghua Zhao, Huijiang Analysis of PDEs We prove global existence of smooth solutions near Maxwellians for the non-cutoff Vlasov-Poisson-Boltzmann system in the weakly collisional regime. To address the weak dissipation of the non-cutoff linearized Boltzmann operator, we develop a refined velocity-weighted energy framework combined with vector-field techniques to control the transport term, nonlinear collisions, and the self-consistent electric field. This approach yields uniform-in-time bounds, captures enhanced dissipation of the solution, and establishes Landau damping for both the density and electric field, providing the first global-in-time result of this type for the non-cutoff Vlasov-Poisson-Boltzmann system. Our approach is inspired by the recent work of Chaturvedi-Luk-Nguyen ({\it J. Amer. Math. Soc.} {\bf 36} (2023), no. 4, 1103--1189.) |
| title | The non-cutoff Vlasov-Poisson-Boltzmann system with weak collisions |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2510.03835 |