Global solution to the 3-D inhomogeneous incompressible MHD system with discontinuous density

In this paper, we consider the Cauchy problem of the incompressible MHD system with discontinuous initial density in ${\mathbb R}^3$. We establish the global well-posedness of the MHD system if the initial data satisfies \begin{document}$(ρ_0, u_0, H_0)∈ L^{∞}({\mathbb R}^3)× H^s({\mathbb R}^3)× H^s({\mathbb R}^3)$\end{document} with \begin{document}$\frac{1}{2} and \begin{document}$0 for some small \begin{document}$c>0$\end{document} which only depends on \begin{document}$\underline{ρ}, \overline{ρ}$\end{document} . As a byproduct, we also get the decay estimate of the solution.