Global well-posedness for the 3D incompressible MHD system with a class of large initial data

We study the global well-posedness for the 3D Magnetohydrodynamics (MHD) system with a class of large initial data. This type of data varies slowly in the vertical direction and its norm blows up in the largest critical space ${\dot{B}}_{\infty ,\infty }^{-1}$ at a rate of ${\epsilon }^{\delta -1}$ for $0\le \delta <1$ as ε tends to zero. With this type of data, we prove the system generates global solutions in $R^3$ when $0<\delta <1$. When $\delta =0$, we prove the system is globally well-posed in $T^2\times R$.