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

doi:10.1007/s10473-023-0217-1

数学物理学报(英文版) ›› 2023, Vol. 43 ›› Issue (2): 777-820.doi: 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^1,†, Ning Jiang²

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

收稿日期:2021-07-16 修回日期:2022-02-17 出版日期:2023-03-25 发布日期:2023-04-12
通讯作者: †Zhendong Fang, E-mail: zdfang@scut.edu.cn.
作者简介:Ning Jiang, E-mail: njiang@whu.edu.cn

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^1,†, Ning Jiang²

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

Received:2021-07-16 Revised:2022-02-17 Online:2023-03-25 Published:2023-04-12
Contact: †Zhendong Fang, E-mail: zdfang@scut.edu.cn.
About author:Ning Jiang, E-mail: njiang@whu.edu.cn

摘要/Abstract

摘要： 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.

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

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

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]. 数学物理学报(英文版), 2023, 43(2): 777-820.

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

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

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