Global Well-posedness for 2D non-resistive MHD equations in half-space

This paper focuses on the initial boundary value problem of two-dimensional non-resistive MHD equations in a half space. We prove that the MHD equations have a unique global strong solution around the equilibrium state $(0,{\mathbf{e}}_{\mathbf{1}})$ for Dirichlet boundary condition of velocity and modified Neumann boundary condition of magnetic.