The incompressible MHD system with external forces in the whole space \(\mathbb {R}^n\) ( \(n \ge 2\) ) is considered. We show the unique existence theorem of local mild solutions to the MHD system for given initial data and external forces in scaling invariant Besov spaces framework. We also obtain global mild solutions for small initial data and external forces. In addition, by assuming suitable additional conditions for initial data and external forces, we reveal that the global mild solutions have some time-decay properties with respect to the scaling invariant norms.
