Well-Posedness for the Three Dimension Magnetohydrodynamic System in the Anisotropic Besov Spaces

Abstract

In this paper, we consider the global well-posedness of the incompressible magnetohydrodynamic system with anisotropic Besov initial data in the critical Besov spaces. Under the nonlinear smallness condition on the critical anisotropic Besov norm of the horizontal components of the initial velocity field and magnetic field, we get the system has a unique global solution. Our result allows to construct global solutions for a class of highly oscillating initial data of Cannone's type.