CONVERGENCE FROM THE TWO-SPECIES VLASOV-POISSON-BOLTZMANN SYSTEM TO THE TWO-FLUID INCOMPRESSIBLE NAVIER-STOKES-FOURIER-POISSON SYSTEM WITH OHM'S LAW&#x0002A;

Zhendong Fang; Ning Jiang

doi:10.1007/s10473-023-0217-1

2023 , Vol. 43 >Issue 2: 777 - 820

DOI: https://doi.org/10.1007/s10473-023-0217-1

CONVERGENCE FROM THE TWO-SPECIES VLASOV-POISSON-BOLTZMANN SYSTEM TO THE TWO-FLUID INCOMPRESSIBLE NAVIER-STOKES-FOURIER-POISSON SYSTEM WITH OHM'S LAW^*

Zhendong Fang ,
Ning Jiang

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1. School of Mathematics, South China University of Technology, Guangzhou 510641, China;
2. School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China

Ning Jiang, E-mail: njiang@whu.edu.cn

Received date: 2021-07-16

Revised date: 2022-02-17

Online published: 2023-04-12

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Abstract

In this paper, we justify the convergence from the two-species Vlasov-Poisson-Boltzmann (VPB, for short) system to the two-fluid incompressible Navier-Stokes-Fourier-Poisson (NSFP, for short) system with Ohm's law in the context of classical solutions. We prove the uniform estimates with respect to the Knudsen number $\varepsilon$ for the solutions to the two-species VPB system near equilibrium by treating the strong interspecies interactions. Consequently, we prove the convergence to the two-fluid incompressible NSFP as $\varepsilon$ goes to 0.

Key words： two-species Vlasov-Poisson-Boltzmann system; global-in-time classical solutions; incompressible Navier-Stokes-Fourier-Poisson system; Ohm's law; uniform energy estimates; convergence

Cite this article

Zhendong Fang , Ning Jiang . CONVERGENCE FROM THE TWO-SPECIES VLASOV-POISSON-BOLTZMANN SYSTEM TO THE TWO-FLUID INCOMPRESSIBLE NAVIER-STOKES-FOURIER-POISSON SYSTEM WITH OHM'S LAW^*[J]. Acta mathematica scientia, Series B, 2023 , 43(2) : 777 -820 . DOI: 10.1007/s10473-023-0217-1

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