This paper is devoted to the large time decay of solutions of a three-dimensional Stokes-Magneto equations. It is shown that, when initial data belong to \(L^2\), weak solutions of the equations decay to zero in \(L^{3/2,\infty }\times L^2\) without a uniform rate, and this decay estimate is optimal. Furthermore, the optimal temporal decay estimates for weak solutions are established when initial data belongs to \(L^1\cap L^2\).

中文翻译：

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三维Stokes-Magneto方程解的长时间行为

本文致力于三维斯托克斯-马涅托方程解的大时间衰减。结果表明，当初始数据属于\（L ^ 2 \）时，方程的弱解在\（L ^ {3/2，\ infty} \ times L ^ 2 \）中衰减为零，且速率不一致。 ，并且此衰减估算值是最佳的。此外，当初始数据属于\（L ^ 1 \ cap L ^ 2 \）时，建立了针对弱解的最优时间衰减估计。