Abstract
The present paper is devoted to the well-posedness issue of solutions of a full system of the 3-D incompressible magnetohydrodynamic (MHD) equations with large initial velocity and magnetic field slowly varying in one space variable. By means of the anisotropic Littlewood-Paley analysis we prove the global well-posedness of solutions in the framework of anisotropic type Besov spaces. In the second part, we prove the global wellposedness of such system with some large data which are slowly varying in one direction.
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