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arXiv · 2510.03835

The non-cutoff Vlasov-Poisson-Boltzmann system with weak collisions

Yuanjie Lei·Shuangqian Liu·Qinghua Xiao·Huijiang Zhao
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Abstract

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.)

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Yuanjie Lei, Shuangqian Liu, Qinghua Xiao, Huijiang Zhao. 2025-10-04. The non-cutoff Vlasov-Poisson-Boltzmann system with weak collisions. https://arxiv.org/abs/2510.03835

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