# American Institute of Mathematical Sciences

doi: 10.3934/dcdsb.2021231
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## Convergence from two-species Vlasov-Poisson-Boltzmann system to two-fluid incompressible Navier-Stokes-Fourier-Poisson system

 1 School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China 2 School of Mathematics and Physics, Wuhan Institute of Technology, Wuhan 430072, China

* Corresponding author: Hao Wang

Received  April 2021 Revised  July 2021 Early access September 2021

In this paper, we obtain the uniform estimates with respect to the Knudsen number $\varepsilon$ for the fluctuations $g^{\pm}_{\varepsilon}$ to the two-species Vlasov-Poisson-Boltzmann (in briefly, VPB) system. Then, we prove the existence of the global-in-time classical solutions for two-species VPB with all $\varepsilon \in (0,1]$ on the torus under small initial data and rigorously derive the convergence to the two-fluid incompressible Navier-Stokes-Fourier-Poisson (in briefly, NSFP) system as $\varepsilon$ go to 0.

Citation: Zhendong Fang, Hao Wang. Convergence from two-species Vlasov-Poisson-Boltzmann system to two-fluid incompressible Navier-Stokes-Fourier-Poisson system. Discrete & Continuous Dynamical Systems - B, doi: 10.3934/dcdsb.2021231
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