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.