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

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 Ohms law in a mathematically rigorous way via the spectral analysis and energy methods.