This paper investigates the global existence of smooth solutions near the equilibrium state \((x_3,0)\) for the Cauchy problem of the incompressible MHD-type equations without magnetic diffusion in the whole space \(\mathbb {R}^3\) . In a prior work by Ren–Xiang–Zhang [Sci. China Math. 59 (2016), pp.1949-1974], the global existence and decay estimates of smooth solutions were established under a high regularity assumption on the initial data, namely \((u_0,\nabla \psi _0)\in H^{14}\) . In this paper, by employing the energy method with temporal weights in conjunction with anisotropic interpolation techniques, we prove the global existence of smooth solutions while significantly relaxing the regularity requirements on the initial data. As a by-product, we also derive explicit time decay rates for the solutions.
