General evolution equations in Banach spaces are investigated. Based on an operator-valued version of de Leeuw’s transference principle, time-periodic \(\mathrm {L}_{p}\) estimates of maximal regularity type are carried over from ℛ-bounds of the family of solution operators (ℛ-solvers) to the corresponding resolvent problems. With this method, existence of time-periodic solutions to the Navier-Stokes equations is shown for two configurations: in a periodically moving bounded domain and in an exterior domain, subject to prescribed time-periodic forcing and boundary data.

中文翻译：

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ℛ-有界性的周期性 $\mathrm{L}_{p}$ 估计：在纳维-斯托克斯方程中的应用

研究了 Banach 空间中的一般演化方程。基于 de Leeuw 转移原理的算子值版本，最大正则类型的时间周期\(\mathrm {L}_{p}\)估计是从解算子族 (ℛ-求解器）到相应的已解决问题。通过这种方法，可以显示两种配置下纳维-斯托克斯方程的时间周期解的存在性：在周期性移动的有界域中和在外部域中，受规定的时间周期强迫和边界数据的影响。