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Stability of Nonlinear Wave Patterns to the Bipolar VlasovPoissonBoltzmann System

Hailiang Li Yi Wang Tong Yang Mingying Zhong

Analysis of PDEs mathscidoc:1912.431001

Archive for Rational Mechanics and Analysis, 228, (1), 39-127, 2018.4
The main purpose of the present paper is to investigate the nonlinear stability of viscous shock waves and rarefaction waves for the bipolar VlasovPoissonBoltzmann (VPB) system. To this end, motivated by the micromacro decomposition to the Boltzmann equation in Liu and Yu (Commun Math Phys 246:133179, 2004) and Liu etal. (Physica D 188:178192, 2004), we first set up a new micromacro decomposition around the local Maxwellian related to the bipolar VPB system and give a unified framework to study the nonlinear stability of the basic wave patterns to the system. Then, as applications of this new decomposition, the time-asymptotic stability of the two typical nonlinear wave patterns, viscous shock waves and rarefaction waves are proved for the 1D bipolar VPB system. More precisely, it is first proved that the linear superposition of two Boltzmann shock profiles in the first and third
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@inproceedings{hailiang2018stability,
  title={Stability of Nonlinear Wave Patterns to the Bipolar VlasovPoissonBoltzmann System},
  author={Hailiang Li, Yi Wang, Tong Yang, and Mingying Zhong},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224211142247874565},
  booktitle={Archive for Rational Mechanics and Analysis},
  volume={228},
  number={1},
  pages={39-127},
  year={2018},
}
Hailiang Li, Yi Wang, Tong Yang, and Mingying Zhong. Stability of Nonlinear Wave Patterns to the Bipolar VlasovPoissonBoltzmann System. 2018. Vol. 228. In Archive for Rational Mechanics and Analysis. pp.39-127. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224211142247874565.
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