Cauchy problem for the VlasovPoissonBoltzmann system

Tong Yang Hongjun Yu Huijiang Zhao

Analysis of PDEs mathscidoc:1912.43940

Archive for rational mechanics and analysis, 182, (3), 415-470, 2006.11
The dynamics of dilute electrons can be modelled by the fundamental VlasovPoissonBoltzmann system which describes mutual interactions of the electrons through collisions in the self-consistent electric field. In this paper, it is shown that any smooth perturbation of a given global Maxwellian leads to a unique global-in-time classical solution when either the mean free path is small or the background charge density is large. Moreover, the solution converges to the global Maxwellian when time tends to infinity. The analysis combines the techniques used in the study of conservation laws with the decomposition of the Boltzmann equation introduced in [17, 19] by obtaining new entropy estimates for this physical model.
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@inproceedings{tong2006cauchy,
  title={Cauchy problem for the VlasovPoissonBoltzmann system},
  author={Tong Yang, Hongjun Yu, and Huijiang Zhao},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224210802165409504},
  booktitle={Archive for rational mechanics and analysis},
  volume={182},
  number={3},
  pages={415-470},
  year={2006},
}
Tong Yang, Hongjun Yu, and Huijiang Zhao. Cauchy problem for the VlasovPoissonBoltzmann system. 2006. Vol. 182. In Archive for rational mechanics and analysis. pp.415-470. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224210802165409504.
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