In this paper we derive the global existence of smooth solutions to the 3D generalized Hall-MHD equations for a class of large initial data, whose \(L^{\infty }\) norms can be arbitrarily large. In addition, we give an example to show that such a large initial value does exist. Our idea is splitting the generalized heat equations from generalized Hall-MHD system to generate a small quantity for large time \(t\).

中文翻译：

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3D广义Hall-MHD方程的一类大型解

在本文中，我们推导了针对一类大初始数据的3D广义Hall-MHD方程的光滑解的全局存在性，其\（L ^ {\ infty} \）范数可以任意大。另外，我们举一个例子来说明确实存在如此大的初始值。我们的想法是将广义热方程从广义Hall-MHD系统中分解出来，以在大时间内\（t \）生成少量热量。