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Global Existence and Long-Time Behavior of Solutions to the Vlasov–Poisson–Fokker–Planck System

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Abstract

In this paper, we study the global existence of solutions to the Vlasov–Poisson–Fokker–Planck system in the whole space by using the refined energy method. In the proof, the a priori estimates on the macroscopic and microscopic components of solutions are obtained by use of the macroscopic balance laws. As a by-product, the algebraic decay rate of solutions converge to the global Maxwellian, which established by employing the Fourier analysis.

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Acknowledgement

The work is supported by the National Natural Science Foundation of China under Grant No. 41962019. The author would like to thank the referee for the valuable comments and suggestions.

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  1. Department of Mathematics, East China University of Technology, Nanchang, 330013, China

    Xiaolong Wang

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  1. Xiaolong Wang
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Correspondence to Xiaolong Wang.

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Wang, X. Global Existence and Long-Time Behavior of Solutions to the Vlasov–Poisson–Fokker–Planck System. Acta Appl Math 170, 853–881 (2020). https://doi.org/10.1007/s10440-020-00361-7

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  • DOI: https://doi.org/10.1007/s10440-020-00361-7

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