Regularity of the $3D$ stationary Hall magnetohydrodynamic equations on the plane

Abstract

We study the regularity of weak solutions to the 3D valued stationary Hall magnetohydrodynamic equations on ${\mathbb{R}}^2$. We prove that every weak solution is smooth. Furthermore, we prove a Liouville type theorem for the Hall equations.

18 pages

References in corpus (2)

• On the weak solutions to the Maxwell-Landau-Lifshitz equations and to the Hall-Magneto-Hydrodynamic equations
• On partial regularity for the steady Hall magnetohydrodynamics system

Cited by in corpus (3)

• Dyadic models with intermittency dependence for the Hall MHD
• Derivation of the Hall-MHD equations from the Navier-Stokes-Maxwell equations
• On the regularity of magneto-vorticity field and the global existence for the Hall magnetohydrodynamic equations