Global regularity for the 2D incompressible MHD-α system without full dissipation and magnetic diffusions

In this paper, we consider the global regularity for the 2D incompressible MHD-α system without full dissipation and magnetic diffusions. We establish the global regularity of classical solutions for the MHD-α system with mixed partial dissipation and magnetic diffusion (ν1=0, ν2>0, η1>0, η2=0) or horizontal dissipation and horizontal magnetic diffusion (ν1>0, ν2=0, η1>0, η2=0). As α→0, the solution converges to that of the corresponding MHD equations. We also obtain the convergence rate of the limit as α→0 in L2-norm.