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

Abstract

We prove the global existence of the smooth solutions near equilibrium to the Cauchy problem of the incompressible non-resistive magnetohydrodynamic equations 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 new proof based on the temporal weighted energy method.