The Global Well-posedness of Strong Solutions to 2D MHD Equations in Lei-Lin Space

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 χ −1 (ℝ 2 ) with any initial data in χ −1 (ℝ 2 ) ∩ L 2 (ℝ 2 ) is established. Furthermore, the uniqueness of the strong solution in χ −1 (ℝ 2 ) and the Leray-Hopf weak solution in L 2 (ℝ 2 ) is proved.