Abstract In this paper, we study the decay properties of a weak solution to the nonstationary Navier-Stokes equations by means of the spectral decomposition method of fractional powers of the Stokes operator, in an arbitrary unbounded domain. The explicit L 2 -decay rates are given as t ⟶ ∞ , which improves greatly the decay results in [8] , [9] .

中文翻译：

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一般无界域中 3D Navier-Stokes 方程弱解的代数衰减

摘要 在本文中，我们利用Stokes 算子的分数幂的谱分解方法，在任意无界域中研究了非平稳Navier-Stokes 方程弱解的衰减特性。显式的 L 2 -衰减率由 t ⟶ ∞ 给出，这极大地改善了 [8] , [9] 中的衰减结果。