In this paper we consider the compressible models of magnetohydrodynamic flows giving rise to a variety of mathematical problems in many areas. We study the asymptotic limit for the compressible rotational magnetohydrodynamic flows with the well-prepared initial data such that we derive a rigorous quasi-geostrophic equation with diffusion term governed by the magnetic field from a compressible rotational magnetohydrodynamic flows. This paper covers two results: the existence of the unique global strong solution of quasi-geostrophic equation with good regularity on the velocity and magnetic field and the derivation of quasi-geostrophic equation with diffusion.

中文翻译：

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旋转可压缩磁流体动力流的渐近极限

在本文中，我们考虑了磁流体动力流的可压缩模型，这些模型在许多领域引起了各种数学问题。我们使用充分准备的初始数据研究可压缩旋转磁流体动力流的渐近极限，以便从可压缩旋转磁流体动力流导出严格的准地转方程，其扩散项受磁场控制。本文涵盖两个结果：存在对速度和磁场具有良好规律性的拟地转方程的唯一整体强解和存在扩散的拟地转方程的推导。