The non-cutoff Vlasov-Poisson-Boltzmann system with weak collisions
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.)
Cite
@article{arxiv.2510.03835,
title = {The non-cutoff Vlasov-Poisson-Boltzmann system with weak collisions},
author = {Yuanjie Lei and Shuangqian Liu and Qinghua Xiao and Huijiang Zhao},
journal= {arXiv preprint arXiv:2510.03835},
year = {2025}
}