Global strong solutions of the density-dependent incompressible MHD system with zero resistivity in a bounded domain

In this paper, we first establish a regularity criterion for the strong solutions to the density-dependent incompressible MHD system with zero resistivity in a bounded domain. Then we use it and the bootstrap argument to prove the global well-posedness provided that the initial data u0 and b0 satisfy that (d-2)||∇u0 || L2+||b0||w1,p are sufficiently small with . We do not assume the positivity of initial density, it may vanish in an open subset (vacuum) of Ω.