Preprint 2004-027

Cauchy Problem for the Vlasov-Poisson-Boltzmann System

Tong Yang, Hongjun Yu, and Huijiang Zhao

Abstract: The dynamics of the dilute electrons can be modeled by the fundamental Vlasov-Poisson-Boltzmann system when the electrons interact with themselves through collisions in the self-consistent electric field. In this paper, it is shown that any smooth initial 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. And the solution converges to the global Maxwellian when time tends to infinity. To our knowledge, this is the first global existence result on classical solutions not around vacuum to the Cauchy problem for the Vlasov-Poisson-Boltzmann system. The analysis combines the analytic techniques used in the study of conservation laws with the decomposition for the Boltzmann equation introduced in [16] through entropy construction revealing new entropy estimates in this physical setting.

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Tong Yang, <>
Hongjun Yu, <>
Huijiang Zhao, <>
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<> May 26 2004.

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