We investigate the local-in-time existence results of classical solutions to the 3D (Hall-)MHD equations with power-law type nonlinear viscous fluid when magnetic resistance is vanished and also show the global-in-time existence of classical solutions under small initial data. Moreover, we prove the space-time decay property for these solutions.

中文翻译：

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某类型幂律型3D Hall-MHD方程的存在性、唯一性及衰减率

我们研究了幂律型非线性粘性流体的 3D (Hall-)MHD 方程在磁阻消失时经典解的局部时间存在性结果，并展示了小磁阻下经典解的全局时间存在性。初始数据。此外，我们证明了这些解的时空衰减特性。