A New Boundary Condition for the Hall-Magnetohydrodynamics Equation with the Ion-Slip Effect

Abstract

In this paper, we prove a regularity criteria and the local well-posedness of strong solutions to the magnetohydrodynamics with the Hall and ion-slip effects in a smooth bounded domain. Moreover, for the magnetohydrodynamics with the Hall effect and without ion-slip effect, we prove the global stability of strong large solutions. These results are obtained under an integrable property that depends on a new vorticity boundary condition which is motivated by the generalized Navier-slip boundary condition involving the vorticity.