In this paper, we study the strong solutions to the Cauchy problem of nonhomogeneous incompressible magnetohydrodynamic (MHD) equations on the whole two-dimensional (2D) space with vacuum as far field density. In particular, the initial density can have compact support. If both the initial density and the initial magnetic field decay not too slow at infinity, the 2D Cauchy problem of the nonhomogeneous incompressible MHD equations admits a unique local strong solution.

中文翻译：

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真空非齐次磁流体动力学方程二维柯西问题的强解

在本文中，我们在以真空为远场密度的整个二维（2D）空间上研究非齐次不可压缩磁流体动力学（MHD）方程的柯西问题的强解。特别地，初始密度可以具有紧凑的支撑。如果初始密度和初始磁场在无穷远处衰减不太慢，则非齐次不可压缩 MHD 方程的二维柯西问题承认唯一的局部强解。