Diffusion Limit with Optimal Convergence Rate of Classical Solutions to the modified Vlasov-Poisson-Boltzmann System

TL;DR

This paper investigates the diffusion limit of classical solutions to the modified Vlasov-Poisson-Boltzmann system, establishing convergence to an incompressible Navier-Stokes-Poisson-Fourier system with precise initial layer estimates.

Contribution

It provides a spectral analysis-based proof of convergence and the rate of classical solutions to the mVPB system towards a fluid dynamic system.

Findings

Proves convergence of solutions to the incompressible Navier-Stokes-Poisson-Fourier system.

Estimates the convergence rate and initial layer effects.

Analyzes the diffusion limit with spectral methods.

Abstract

In the present paper, we study the diffusion limit of the classical solution to the modified Vlasov-Poisson-Boltzmann (mVPB) System with initial data near a global Maxwellian. Based on the spectral analysis, weprove the convergence and establish the convergence rate of the global strong solution to the mVPB system towards the solution to an incompressible Navier-Stokes-Poisson-Fourier system with the precise estimation on the initial layer.