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

摘要

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