Methods and Applications of Analysis
Volume 29 (2022)
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
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.
Vlasov–Poisson–Boltzmann system, rarefaction waves, macro-micro decomposition, energy method
2010 Mathematics Subject Classification
35B35, 35B40, 35Q20, 76P05
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