In this paper, we study the well-posedness of boundary layer problems for the inhomogeneous incompressible magnetohydrodynamics (MHD) equations, which are derived from the two-dimensional density-dependent incompressible MHD equations. Under the assumption that initial tangential magnetic field is not zero and density is a small perturbation of the outer constant flow in supernorm, the local-in-time existence and uniqueness of inhomogeneous incompressible MHD boundary layer equations are established in weighted conormal Sobolev space by energy method.

中文翻译：

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二维非均匀不可压缩磁流体动力学方程的边界层问题

在本文中，我们研究了非均质不可压缩磁流体动力学（MHD）方程的边界层问题的适定性，该方程是从二维依赖于密度的不可压缩MHD方程导出的。在初始切向磁场不为零且密度为超常模中外部恒定流的微小扰动的假设下，通过能量在加权的标准Sobolev空间中建立了非均匀不可压缩MHD边界层方程的局部时间存在性和唯一性方法。