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Global Existence of Classical Solutions to the Vlasov-Poisson-Boltzmann System

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Abstract

The time evolution of the distribution function for the charged particles in a dilute gas is governed by the Vlasov–Poisson–Boltzmann 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 Navier–Stokes 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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Authors and Affiliations

  1. Liu Bie Ju Centre for Mathematical Sciences, City University of Hong Kong, Tat Chee Avenue, Kowloon, Hong Kong

    Tong Yang

  2. School of Mathematics and Statistics, Wuhan University, Wuhan, 430072, China

    Huijiang Zhao

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  1. Tong Yang
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  2. Huijiang Zhao
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Correspondence to Tong Yang.

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Communicated by H.-T. Yau.

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Yang, T., Zhao, H. Global Existence of Classical Solutions to the Vlasov-Poisson-Boltzmann System. Commun. Math. Phys. 268, 569–605 (2006). https://doi.org/10.1007/s00220-006-0103-4

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  • DOI: https://doi.org/10.1007/s00220-006-0103-4

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