Global mild solutions to three-dimensional magnetohydrodynamic system in Morrey spaces

Abstract

In this article, the Cauchy problem of three-dimensional (3-D) incompressible magnetohydrodynamic system was investigated. If the initial ${\mathcal{M}}^{1,1}$ norms of the vorticity $\omega$ and the current density $j$ are both sufficiently small, then some uniform estimates with respect to time for the coupling terms between the fluid and the magnetic field can be established, which lead to a global-in-time well-posedness of mild solutions in Morrey spaces via some effective arguments.