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

TL;DR

This paper investigates the diffusion limit of classical solutions to the Vlasov-Maxwell-Boltzmann system, establishing optimal convergence rates to the Navier-Stokes-Maxwell system through spectral analysis and a novel solution decomposition.

Contribution

It introduces a new decomposition method to identify initial layer components and proves the optimal convergence rate of solutions from the VMB system to the Navier-Stokes-Maxwell system.

Findings

Proves convergence of VMB solutions to Navier-Stokes-Maxwell solutions.

Establishes the optimal convergence rate.

Introduces a new decomposition technique for the solution.

Abstract

We study the diffusion limit of the strong solution to the Vlasov-Maxwell-Boltzmann (VMB) system with initial data near a global Maxwellian. By introducing a new decomposition of the solution to identify the essential components for generating the initial layer, we prove the convergence and establish the opitmal convergence rate of the classical solution to the VMB system to the solution of the Navier-Stokes-Maxwell system based on the spectral analysis.