A body \(\mathscr {B}\) is started from rest by a translational motion in an otherwise quiescent Navier–Stokes liquid filling the whole space. We show, for small data, that if after some time \(\mathscr {B}\) reaches a spinless oscillatory motion of period \(\mathcal T\), the liquid will eventually execute also a time periodic motion with the same period \(\mathcal T\). This result is a suitable generalization of the famous Finn’s starting problem for steady states, to the case of time-periodic motions.

中文翻译：

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粘性液体经过振荡体的周期性流动的可达到性

物体\（\ mathscr {B} \）在静止的Navier–Stokes液体中通过平移运动从静止开始，该液体充满整个空间。对于小数据，我们表明，如果一段时间后\（\ mathscr {B} \）达到周期\（\ mathcal T \）的无旋振荡运动，液体最终还将最终执行相同周期的时间周期运动\（\数学T \）。对于时间周期运动，此结果是对稳态的著名Finn起始问题的适当推广。