Global well-posedness and analyticity for the 3D fractional magneto-hydrodynamics equations in the Besov-Morrey spaces caracerized by Semi-group

Our research establishes the existence and uniqueness of solutions, the analyticity, and the decay estimates of the solutions of the 3D fractional magneto-hydrodynamics equations (FMHD) in the BesovMorrey spaces characterized by the semigroup Lα := e-t(-∆)α, noted by Ns p,λ. Assuming that the initial data (a0, m0) are small and belong to Ns p,λ, we prove the global well-posedness of the (FMHD) equation.