The global well-posedness for the 2D Leray-. MHD equations with zero magnetic diffusivity

By means of Fourier frequency localization and Bony.s paraproduct decomposition, we study the global existence and the uniqueness of the 2D Leray-. Magneta-hydrodynamics model with zero magnetic diffusivity for the general initial data. In view of the profits bring by the . model, then using the energy estimate in the frequency space and the Logarithmic Sobolev inequality, we obtain the estimate .t0..u.L.ds which is crucial to get the global existence for the general initial data.