Existence of global axisymmetric solutions for a 3D inhomogeneous incompressible hall-magnetohydrodynamic system

We study the global well-posedness of an inhomogeneous incompressible Hall-MHD system in the whole space R 3 .Let 0 be the initial density of the fluids.Under certain appropriate smallness assumptions on a 0 /r, where a 0 = (1/ 0 )-1 and r = (x 2 1 +x 2 2 ) 1/2 , we demonstrate the global regularity of the solutions to the Cauchy problem of the inhomogeneous Hall-MHD system with axisymmetric initial data, where the swirl component of the velocity field and magnetic vorticity field vanish.