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Diffusion Limit and the optimal convergence rate of the classical solution to the one-species Vlasov-Maxwell-Boltzmann system

Ke Chen, Anita Yang, Mingying Zhong

Abstract

In the present paper, we study the diffusion limit of the strong solution to the one-species Vlasov-Maxwell-Boltzmann (VMB) system with initial data near a global Maxwellian. Based on spectral analysis techniques, we prove the convergence and establish the convergence rate of the classical solution to the VMB system towards the solution to the incompressible Navier--Stokes--Maxwell system with a precise estimation on the initial layer.

Diffusion Limit and the optimal convergence rate of the classical solution to the one-species Vlasov-Maxwell-Boltzmann system

Abstract

In the present paper, we study the diffusion limit of the strong solution to the one-species Vlasov-Maxwell-Boltzmann (VMB) system with initial data near a global Maxwellian. Based on spectral analysis techniques, we prove the convergence and establish the convergence rate of the classical solution to the VMB system towards the solution to the incompressible Navier--Stokes--Maxwell system with a precise estimation on the initial layer.
Paper Structure (4 sections, 2 theorems, 90 equations)

This paper contains 4 sections, 2 theorems, 90 equations.

Table of Contents

  1. Introduction
  2. Spectral analysis
  3. Spectrum structure
  4. Semigroup of the linear NSMF system

Key Result

Theorem 1.1

For any $\epsilon\in (0,1)$, there exists a small constant $\delta_0>0$ such that if the initial data $U_0=(f_0,E_0,B_0)$ satisfy that $\|U_{0}\|_{ X^5_1 }+\|U_{0}\|_{L^1 } \le \delta_0$, then the VMB system VMB4--VMB2i admits a unique global solution $U_{\epsilon}(t,x,v)= (f_{\epsilon},E_{\epsilon} There exists a small constant $\delta_0>0$ such that if $\|U_{0}\|_{H^4 }+\|U_{0}\|_{L^1 } \le \del

Theorems & Definitions (6)

  • Theorem 1.1
  • Theorem 1.2
  • proof
  • proof
  • proof
  • proof