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Global existence of classical solutions to the Vlasov-Poisson-Boltzmann system

Tong Yang Huijiang Zhao

Analysis of PDEs mathscidoc:1912.43938

Communications in mathematical physics, 268, (3), 569-605, 2006.12
The time evolution of the distribution function for the charged particles in a dilute gas is governed by the VlasovPoissonBoltzmann system when the force is self-induced and its potential function satisfies the Poisson equation. In this paper, we give a satisfactory global existence theory of classical solutions to this system when the initial data is a small perturbation of a global Maxwellian. Moreover, the convergence rate in time to the global Maxwellian is also obtained through the energy method. The proof is based on the theory of compressible NavierStokes equations with forcing and the decomposition of the solutions to the Boltzmann equation with respect to the local Maxwellian introduced in [23] and elaborated in [31].
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@inproceedings{tong2006global,
  title={Global existence of classical solutions to the Vlasov-Poisson-Boltzmann system},
  author={Tong Yang, and Huijiang Zhao},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224210756350559502},
  booktitle={Communications in mathematical physics},
  volume={268},
  number={3},
  pages={569-605},
  year={2006},
}
Tong Yang, and Huijiang Zhao. Global existence of classical solutions to the Vlasov-Poisson-Boltzmann system. 2006. Vol. 268. In Communications in mathematical physics. pp.569-605. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224210756350559502.
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