In this expository paper, we study $L^q$-$L^r$ decay estimates of the evolution operator generated by a perturbed Stokes system in n-dimensional exterior domains when the coefficients are time-dependent and can be unbounded at spatial infinity. By following the approach developed by the present author for the physically relevant case where the rigid motion of the obstacle is time-dependent, we clarify that some decay properties of solutions to the same system in whole space ${\mathbb{R}}^n$ together with the energy relation imply the desired estimates in exterior domains provided $n\ge 3$.

中文翻译：

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外部域中线性非自治系统解的大时间衰减

在这篇说明性论文中，我们研究了 ${\mathrm{大号}}^q$--${\mathrm{大号}}^{\mathrm{[R}}$当系数是随时间变化的并且在空间无穷大处是无穷大时，由扰动的Stokes系统在n维外部域中生成的演化算子的​​衰减估计。通过遵循本作者针对障碍物的刚性运动与时间相关的物理相关情况开发的方法，我们阐明了在整个空间中同一系统的解的某些衰减性质${\mathbb{[R}}^{ñ}$ 与能量关系一起意味着在提供的外部域中进行所需的估计 $ñ\ge 3$。