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Global mild solutions to three-dimensional magnetohydrodynamic system in Morrey spaces (2003.10786v1)
Published 24 Mar 2020 in math.AP
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.