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 for ϵ and σ sufficiently small. Toward this and due to the divergence-free property of magnetic field, the proof is based on unified energy estimates which is valid for the magnetic field satisfying the inhomogeneous damped wave equation.
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