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.

中文翻译：

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Vlasov-Poisson-Fokker-Planck系统解的全局存在性和长期行为

在本文中，我们使用精细能量方法研究了整个空间中Vlasov-Poisson-Fokker-Planck系统解的全局存在性。在证明中，通过使用宏观平衡定律可以获得对溶液的宏观和微观成分的先验估计。作为副产品，解决方案的代数衰减率收敛于通过采用傅立叶分析建立的整体麦克斯韦方程。