Convergence from two-species Vlasov-Poisson-Boltzmann system to two-fluid incompressible Navier-Stokes-Fourier-Poisson system with Ohm's law

TL;DR

This paper rigorously proves the convergence of the two-species Vlasov-Poisson-Boltzmann system to the two-fluid incompressible Navier-Stokes-Fourier-Poisson system with Ohm's law, using uniform estimates near equilibrium.

Contribution

It establishes the convergence from kinetic to fluid models for the two-species VPB system with strong interspecies interactions, a novel result in this context.

Findings

Uniform estimates for solutions near equilibrium

Convergence as Knudsen number approaches zero

Validation of fluid dynamic limit for two-species VPB system

Abstract

In this paper, we justify the convergence from the two-species Vlasov-Poisson-Boltzmann (in briefly,VPB) system to the two-fluid incompressible Navier-Stokes-Fourier-Poisson (in briefly, NSFP) 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 $\varepsilon$ go to 0.