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We prove the global existence of the smooth solutions near equilibrium to theCauchy problem of the incompressible non-resistive magnetohydrodynamicequations in the whole three dimensional space under some admissible condition.The result has been obtained by Xu and Zhang (SIAM J. Math. Anal. 47: 26--65,2015) in anisotropic Besov space framework. In this paper, we provide a newproof based on the temporal weighted energy method.

On the energy method for the global solutions to the three dimensional incompressible non-resistive MHD near equilibrium