Weak collision effect on nonlinear Landau damping for the Vlasov-Poisson-Fokker-Planck system
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866917916561113088 |
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| author | Luo, Yue |
| author_facet | Luo, Yue |
| contents | We investigate the impact of weak collisions on Landau damping in the Vlasov-Poisson-Fokker-Planck system on a torus, specifically focusing on its proximity to a Maxwellian distribution. In the case where the Gevrey index satisfies $\frac{1}{s}\leq3$, we establish the global stability and enhanced dissipation of small initial data, which remain unaffected by the small diffusion coefficient $ν$. For Gevrey index $\frac{1}{s}>3$, we prove the global stability and enhanced dissipation of initial data, whose size is on the order of $O(ν^\frac{1-3s}{3-3s})$. Our analysis provides insights into the effects of phase mixing, enhanced dissipation, and plasma echoes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_05601 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Weak collision effect on nonlinear Landau damping for the Vlasov-Poisson-Fokker-Planck system Luo, Yue Analysis of PDEs We investigate the impact of weak collisions on Landau damping in the Vlasov-Poisson-Fokker-Planck system on a torus, specifically focusing on its proximity to a Maxwellian distribution. In the case where the Gevrey index satisfies $\frac{1}{s}\leq3$, we establish the global stability and enhanced dissipation of small initial data, which remain unaffected by the small diffusion coefficient $ν$. For Gevrey index $\frac{1}{s}>3$, we prove the global stability and enhanced dissipation of initial data, whose size is on the order of $O(ν^\frac{1-3s}{3-3s})$. Our analysis provides insights into the effects of phase mixing, enhanced dissipation, and plasma echoes. |
| title | Weak collision effect on nonlinear Landau damping for the Vlasov-Poisson-Fokker-Planck system |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2401.05601 |