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arXiv · 2401.05601

Weak collision effect on nonlinear Landau damping for the Vlasov-Poisson-Fokker-Planck system

Yue Luo
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Abstract

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 $\nu$. 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 $O(\nu^\frac{1-3s}{3-3s})$. Our analysis provides insights into the effects of phase mixing, enhanced dissipation, and plasma echoes.

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Yue Luo. 2024-01-11. Weak collision effect on nonlinear Landau damping for the Vlasov-Poisson-Fokker-Planck system. https://arxiv.org/abs/2401.05601

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