We investigate the initial value problem for the three dimensional generalized incompressible MHD system. Analyticity of global solutions was proved by energy method in the Fourier space and continuous argument. Then decay rate of global small solutions in the function space $ \mathcal {X}^{1-2\alpha}\bigcap \mathcal {X}^{1-2\beta} $ follows by constructing time weighted energy inequality.

中文翻译：

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三维广义MHD系统整体解的衰减率

我们研究了三维广义不可压缩MHD系统的初值问题。通过傅立叶空间中的能量方法和连续论证证明了整体解的解析性。然后，通过构造时间加权能量不等式，遵循函数空间$ \ mathcal {X} ^ {1-2 \ alpha} \ bigcap \ mathcal {X} ^ {1-2 \ beta} $的全局小解的衰减率。