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.

中文翻译：

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带真空的可压缩非电阻磁流体动力学方程的二维柯西问题的局部强解

本文涉及在真空为远场密度的情况下，整个二维空间上可压缩的非电阻性磁流体动力学方程的柯西问题。当剪切粘度和体积粘度分别为正常数和密度的幂函数时，我们证明只要初始密度和初始磁场在无限远处衰减不太慢，就存在唯一的局部强解。特别是，不需要任何Cho-Choe-Kim类型兼容性条件。