We study the global existence of classical solutions for two-dimensional
incompressible MHD system with only magnetic diffusion. By using the
time-weighted lower-order energy and uniformly bounded higher-order energy
estimates, we prove the global existence result under the assumption that the
initial magnetic field is close enough to a constant magnetic vorticity
equilibrium.Comment: 20 pages. arXiv admin note: text overlap with arXiv:2310.1091