Global Well-Posedness for the 2-D MHD Equations with Magnetic Diffusion

Abstract

In this paper, we consider the 2-D MHD equations with magnetic resistivity but without dissipation on the torus. We prove that if the initial data is small in $H^4$($\mathbb{T}^2$), then the 2-D MHD equations are globally well-posed. To our knowledge, this is the first global well-posedness result for this system.