The global well-posedness of strong solutions to 2D MHD equations in Lei-Lin space

Abstract

In this paper, we study the Cauchy problem of the 2D incompressible magnetohydrodynamic equations in Lei-Lin space. The global well-posedness of a strong solution in the Lei-Lin space $\chi^{-1}(\mathbb{R}^2)$ with any initial data in $\chi^{-1}(\mathbb{R}^2)\cap L^2(\mathbb{R}^2)$ is established. Furthermore, the uniqueness of the strong solution in $\chi^{-1}(\mathbb{R}^2)$ and the Leray-Hopf weak solution in $L^2(\mathbb{R}^2)$ is proved.