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 H 1 weak solutions is proved for a general domain, and an infinite number of weak solutions exist if the domain has holes. Existence of H 2 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. [ABSTRACT FROM AUTHOR]