Global existence of strong solutions to the multi-dimensional inhomogeneous incompressible MHD equations

This paper is concerned with the Cauchy problem of multi-dimensional incompressible magnetohydrodynamic equations inhomogeneous density and fractional dissipation. It shown that when α+β=1+n2 satisfying 1≤β≤α≤min{3β2,n2,1+n4} max{n4,n+16}<α for n≥3, MHD have a unique global strong solution initial data in some Sobolev spaces without requiring small conditions.