The Maxwell-Boltzmann approximation for ion kinetic modeling

TL;DR

This paper rigorously justifies the Maxwell-Boltzmann approximation for electrons in ion kinetic models, establishing conditions for its validity and proving the global well-posedness of the reduced ion problem.

Contribution

It provides a mathematical justification for the Maxwell-Boltzmann approximation in ion-electron kinetic models and demonstrates the global well-posedness of the reduced ion equations.

Findings

Maxwell-Boltzmann approximation is valid under specific regularity conditions.

The reduced ion problem is well-posed globally in time.

A precise scaling regime for the approximation is identified.

Abstract

This paper aims to justify the Maxwell-Boltzmann approximation for electrons, preserving the dynamics of ions at the kinetic level. Under sufficient regularity assumption, we provide a precise scaling where the Maxwell-Boltzmann approximation is obtained. In addition, we prove that the reduced ions problem is well-posed globally in time.