We are concerned with the Cauchy problem of two-dimensional (2D) full compressible magnetohydrodynamic (MHD) equations in the whole plane with zero density at infinity. By spatial weighted energy method, we derive the local existence and uniqueness of strong solutions provided that the initial density and the initial magnetic field decay not too slowly at infinity. In particular, vacuum states at both the interior domain and the far field are allowed.

中文翻译：

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无限真空下全可压缩磁流体动力学方程的二维柯西问题的局部适定性

我们关注的是整个平面中的二维 (2D) 全可压缩磁流体动力学 (MHD) 方程的柯西问题，在无穷远处具有零密度。通过空间加权能量方法，我们推导了强解的局部存在性和唯一性，前提是初始密度和初始磁场在无穷远处衰减不太慢。特别是，允许​​内部域和远场的真空状态。