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 Ohm's law in a mathematically rigorous way via the spectral analysis and energy methods

Logarithmically improved regularity criterion for the 3D Hall-MHD equations

In this work, we study the blow-up criterion of the smooth solutions of three-dimensional incompressible Hall-magnetohydrohynamics equations (in short, Hall-MHD). We obtain a logarithmically improved regularity criterion of smooth solutions in terms of the B˙∞,∞0 norm. We improve the blow-up criterion for smooth solutions established in Ye (Appl Anal 96:2669–2683, 2016). © 2021, SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional