Communications in Mathematical Sciences

Volume 22 (2024)

Number 1

Global mild solutions of the non-cutoff Vlasov–Poisson–Boltzmann system

Pages: 113 – 135

DOI: https://dx.doi.org/10.4310/CMS.2024.v22.n1.a5

Authors

Hao Wang (Department of Mathematical Sciences, Tsinghua University, Beijing, China)

Guangqing Wang (School of Mathematics and Statistics, Fuyang Normal University, Fuyang, China)

Abstract

This paper is concerned with the Cauchy problem on the Vlasov–Poisson–Boltzmann system in the torus domain. The Boltzmann collision kernel is assumed to be angular non-cutoff with $0 \leq \gamma \lt 1$ and $1/2 \leq s \lt 1$, where $\gamma, s$ are two parameters describing the kinetic and angular singularities, respectively. We obtain the global-in-time unique mild solutions, and prove that the solutions converge to the global Maxwellian with the large-time decay rate of $\mathcal{O}(e^{-\lambda t})$ in the $L^1_k L^2_v$-norm for some $\lambda \gt 0$. Furthermore, we justify the property of propagation of regularity of solutions in the spatial variable.

Keywords

Vlasov–Poisson–Boltzmann system, non-cutoff, mild regularity, global existence, time decay

2010 Mathematics Subject Classification

35B35, 35Q20, 35Q83

The full text of this article is unavailable through your IP address: 3.22.242.169

Received 13 February 2023

Accepted 8 May 2023

Published 7 December 2023