Global Strong Solutions to Cauchy Problem of 1D Non-resistive MHD Equations with No Vacuum at Infinity

In this paper, we study the Cauchy problem of 1D non-resistive compressible magnetohydrodynamics (MHD) equations. We established the global existence and uniqueness of strong solutions for large initial data, where the initial density and initial magnetic field approach non-zero constants at infinity, but the initial vacuum of the density inside the region can be permitted. The analysis is based on the Caffarelli-Kohn-Nirenberg weighted inequality and the technique of mathematical frequency decomposition to get the upper bound of the density, and no more artificial conditions are needed to obtain the upper bound estimate of magnetic field $b$ .