Diffusion Limit of the Vlasov-Poisson-Boltzmann System

TL;DR

This paper rigorously analyzes the diffusion limit of the unipolar Vlasov-Poisson-Boltzmann system, demonstrating convergence to an incompressible Navier-Stokes-Poisson-Fourier system with explicit rates, under near-Maxwellian initial data.

Contribution

It establishes the convergence and rate of the classical solution of the VPB system to the fluid dynamic system using spectral analysis and initial layer estimates.

Findings

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

Provides explicit convergence rates.

Analyzes initial layer effects in the diffusion limit.

Abstract

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