Derivation of the Hall-MHD equations from the Navier-Stokes-Maxwell equations

TL;DR

This paper rigorously derives the Hall-MHD equations from the Navier-Stokes-Maxwell equations using spectral analysis and energy methods, providing a solid mathematical foundation for the connection between these models.

Contribution

It offers a rigorous derivation of Hall-MHD equations from Navier-Stokes-Maxwell equations, extending previous heuristic or scaled derivations.

Findings

Rigorous derivation of Hall-MHD from Navier-Stokes-Maxwell

Application of spectral analysis and energy methods

Mathematically justified connection between models

Abstract

By using a set of scaling limits, the authors in \cite{ADFL,SS} proposed a framework of deriving the Hall-MHD equations from the two-fluids Euler-Maxwell equations for electrons and ions. In this paper, we derive the Hall-MHD equations from the Navier-Stokes-Maxwell equations with generalized Ohm's law in a mathematically rigorous way via the spectral analysis and energy methods.