In this paper, we study global well-posedness and temporal decay for the generalized magneto-hydrodynamic equations with some large initial data in Besov type spaces. Making full use of algebraic structure of equations, we prove that there exist two positive constants \(c_0\) and \(C_0\) such that if the initial velocity field \(U_0\) and the initial magnetic field \(B_0\) satisfy one of the following conditions: \(\begin{aligned} \big \Vert U_0-B_0\big \Vert _{\dot{B}^{1-2\alpha +\frac{d}{p}}_{p,1}}\exp \big \{C_0 \big \Vert U_0+B_0\big \Vert _{\dot{B}^{1-2\alpha +\frac{d}{q}}_{q,1}} \big \}\le c_0 \end{aligned}\) or \(\begin{aligned} \big \Vert U_0+B_0\big \Vert _{\dot{B}^{1-2\alpha +\frac{d}{q}}_{q,1}}\exp \big \{C_0 \big \Vert U_0-B_0\big \Vert _{\dot{B}^{1-2\alpha +\frac{d}{p}}_{p,1}} \big \}\le c_0, \end{aligned}\) then the generalized magneto-hydrodynamic equations admits a unique global solution. In addition, we establish the optimal decay rates of global solutions by using the Fourier splitting approach and the interpolation techniques.
