This paper considers the large time properties of global solutions to the 3D incompressible magnetohydrodynamic system in critical spaces \({\dot{H}}^\frac{1}{2}({\mathbb {R}}^3)\) and \(L^3({\mathbb {R}}^3)\). More precisely, we obtain the temporal decay rate \((1+t)^{-\frac{1}{4}}\) for a small global solution in the space \({\dot{H}}^\frac{1}{2}({\mathbb {R}}^3)\), and a small global solution in the space \(L^3({\mathbb {R}}^3)\) is non-increasing and decays to zero at infinity.

中文翻译：

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关键空间中3D磁流体动力学系统整体解的时间衰减

本文考虑了3D不可压缩磁流体力学系统在临界空间\（{\ dot {H}} ^ \ frac {1} {2}（{\ mathbb {R}} ^ 3）\）中的整体时间特性和\（L ^ 3（{\ mathbb {R}} ^ 3）\）。更准确地说，我们获得空间\（{\ dot {H}} ^ \ frac中的一个小的全局解的时间衰减率\（（（1 + t）^ {-\ frac {1} {4}} \）{1} {2}（{\ mathbb {R}} ^ 3）\）和空间\（L ^ 3（{\ mathbb {R}} ^ 3）\）中的小全局解是不增加的并在无穷远处衰减为零。