In this paper, based on a perturbation argument and fully exploring the nonlinear structure of the considered system, we establish the global existence to the three-dimensional generalized incompressible Hall-MHD equations for a class of large initial data, whose $L^p,1\le p\le \mathrm{\infty }$ norms can be arbitrarily large. Our obtained result improves considerably the recent result in Li et al. [A class large solution of the 3D Hall-magnetohydrodynamic equations. J Differ Equ. 2020;268(10):5811–5822] to the generalized Hall-MHD system with $0\le \alpha \le 1$ equipping with different viscosity and magnetic diffusion coefficients.

中文翻译：

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具有大数据的 3D 广义霍尔磁流体动力学方程的全局平滑解

在本文中，基于微扰论证并充分探索所考虑系统的非线性结构，我们建立了一类大初始数据的三维广义不可压缩 Hall-MHD 方程的全局存在性，其${\mathrm{大号}}^p,\mathrm{1个}\le p\le \mathrm{\infty }$范数可以任意大。我们获得的结果大大改善了 Li 等人最近的结果。[3D 霍尔磁流体动力学方程的一类大解。J 不同的设备。2020;268(10):5811–5822] 到广义霍尔 MHD 系统$0\le \alpha \le \mathrm{1个}$配备不同的粘度和磁扩散系数。