Steady states of Hall-MHD system

This paper concerns steady states of the resistive incompressible Hall magnetohydrodynamics (Hall-MHD) system, with emphasis on the effect of the Hall term on the solutions. Existence of H1 weak solutions is proved for a general domain, and an infinite number of weak solutions exist if the domain has holes. Existence of H2 weak solutions is proved for either small data or small Hall parameter μ. The asymptotic behavior of the solutions in the vanishing Hall parameter limit is examined, and the asymptotic stability of the steady states is also investigated.