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In this paper, we investigate the Cauchy problem of the compressiblenon-resistive MHD on $\mathbb{R}^2$ with vacuum as far field density. We provethat the 2D Cauchy problem has a unique local strong solution provided theinitial density and magnetic field decay not too slow at infinity. Furthermore,if the initial data satisfies some additional regularity and compatibilityconditions, the strong solution becomes a classical one. Additionally, weestablish a blowup criterion for the 2D compressible non-resistive MHDdepending solely on the density and magnetic fields.

On classical solutions to the Cauchy problem of the 2D compressible non-resistive MHD equations with vacuum