  Whether or not the classical solutions of the two-dimensional (2D)
incompressible magnetohydrodynamics (MHD) equations with only Laplacian
magnetic diffusion (without velocity dissipation) are globally well-posed is a
difficult problem and remains completely open. In this paper, we establish the
global regularity of solutions to the 2D incompressible MHD equations with
almost Laplacian magnetic diffusion in the whole space. This result can be
regarded as a further improvement and generalization of the previous works.
Consequently, our result is more closer to the resolution of the global
regularity issue on the 2D MHD equations with standard Laplacian magnetic
diffusion.
