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.