Global well-posedness and decay results for 3D generalized magneto-hydrodynamic equations in critical Fourier-Besov-Morrey spaces

Abstract

This article concerns the Cauchy problem of the 3D generalized incompressible magneto-hydrodynamic (GMHD) equations. By using the Fourier localization argument and the Littlewood-Paley theory as in [5,31], we obtain global well-posedness results of the GMHD equations with small initial data belonging to the critical Fourier-Besov-Morrey spaces. Moreover, we prove that the corresponding global solution decays to zero as time approaches infinity.