Under the condition of small external forces, we obtain existence of a weak solution of the steady Hall-MHD system with Hölder continuous magnetic field. We also established regularity of weak solutions provided that magnetic fields are bounded. For sufficiently small external forces, uniqueness result is also established.

中文翻译：

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具有稳定磁场Hall-MHD系统的有界磁场的弱解的存在性，规则性和唯一性

在外力较小的情况下，我们获得了带有Hölder连续磁场的稳定Hall-MHD系统的弱解。如果磁场是有界的，我们还建立了弱解的规律性。对于足够小的外力，也建立了唯一性结果。