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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

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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 ε 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 ε goes to 0.

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Authors and Affiliations

  1. School of Mathematics, South China University of Technology, Guangzhou, 510641, China

    Zhendong Fang  (方圳东)

  2. School of Mathematics and Statistics, Wuhan University, Wuhan, 430072, China

    Ning Jiang  (江宁)

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  1. Zhendong Fang  (方圳东)
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  2. Ning Jiang  (江宁)
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Correspondence to Zhendong Fang  (方圳东).

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Fang, Z., Jiang, N. Convergence from the Two-Species Vlasov-Poisson-Boltzmann System to the Two-Fluid Incompressible Navier-Stokes-Fourier-Poisson System with Ohm’s Law. Acta Math Sci 43, 777–820 (2023). https://doi.org/10.1007/s10473-023-0217-1

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

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