On Local Strong Solutions to the 2D Cauchy Problem of the Compressible Non-resistive Magnetohydrodynamic Equations with Vacuum

This paper concerns the Cauchy problem of the compressible non-resistive magnetohydrodynamic equations on the whole two-dimensional space with vacuum as far field density. When the shear and the bulk viscosities are a positive constant and a power function of the density respectively, we prove that there exists a unique local strong solution provided the initial density and the initial magnetic field decay not too slow at infinity. In particular, there is no need to require any Cho–Choe–Kim type compatibility conditions.