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

Fuente: arXiv
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Auteurs principaux: Lei, Yuanjie, Liu, Shuangqian, Xiao, Qinghua, Zhao, Huijiang
Format: Preprint
Publié: 2025
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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