Methods and Applications of Analysis

Volume 29 (2022)

Number 1

Special issue dedicated to Professor Ling Hsiao on the occasion of her 80th birthday, Part IV

Guest editors: Qiangchang Ju (Institute of Applied Physics and Computational Mathematics, Beijing), Hailiang Li (Capital Normal University, Beijing), Tao Luo (City University of Hong Kong), and Zhouping Xin (Chinese University of Hong Kong)

Stability of rarefaction waves for the two-species Vlasov–Poisson–Boltzmann system with soft potentials

Pages: 95 – 148

DOI: https://dx.doi.org/10.4310/MAA.2022.v29.n1.a4

Authors

Dongcheng Yang (School of Mathematical Sciences, South China Normal University, Guangzhou, China)

Hongjun Yu (School of Mathematical Sciences, South China Normal University, Guangzhou, China)

Abstract

In this paper, we construct the global solutions near a local Maxwellian for the onedimensional two-species Vlasov–Poisson–Boltzmann system with soft potentials. The macroscopic components of this local Maxwellian are the approximate rarefaction wave solutions to the associated one-dimensional compressible Euler system. Then we prove the stability of the rarefaction waves for the two-species Vlasov–Poisson–Boltzmann system in the weighted function space. Moreover, some time decay rates of the disparity between two species and the electric field are obtained.

Keywords

Vlasov–Poisson–Boltzmann system, rarefaction waves, macro-micro decomposition, energy method

2010 Mathematics Subject Classification

35B35, 35B40, 35Q20, 76P05

Full Text (PDF format)

The research of the authors was supported by the GDUPS 2017 and by NNSFC Grant 11371151.

Received 14 September 2020

Accepted 15 December 2020

Published 10 June 2022