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

Abstract 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 ( ν 1 = 0 , ν 2 > 0 , η 1 > 0 , η 2 = 0 ) or horizontal dissipation and horizontal magnetic diffusion ( ν 1 > 0 , ν 2 = 0 , η 1 > 0 , η 2 = 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 L 2 -norm.