Global Well-Posedness for the 2-D MHD Equations with Magnetic Diffusion (Communications in Mathematical Research, 2020)
In this paper, we consider the 2-D MHD equations with magneticresistivity but without dissipation on the torus. We prove that if the initial datais small in $H^4$($\mathbb{T}^2$), then the 2-D MHD equations are globally well-posed. Toour knowledge, this is the first global well-posedness result for this system.