Derivation of the Hall-MHD Equations from the Navier–Stokes–Maxwell Equations

By using a set of scaling limits, the authors in Acheritogaray et al. (Kinet Relat Models 4:901–918, 2011) and Srinivasan Shumlak (Phys Plasmas 18(9):620, proposed framework deriving Hall-MHD equations from two-fluids Euler–Maxwell for electrons ions. In this paper, we derive Navier–Stokes–Maxwell with generalized Ohm’s law mathematically rigorous way via spectral analysis energy methods.