Global well-posedness for 2D inviscid and resistive MHD system near an equilibrium

Abstract

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