We study the existence, uniqueness, regularity and asymptotic spatial behavior of a Navier–Stokes flow past a body, $${\mathscr {B}}$$ B , moving by a time-periodic translational motion of period T , and with zero average. For example, $${\mathscr {B}}$$ B moves in an oscillating fashion. We then show that the flow is also time-periodic with same period T . However, sufficiently “far” from the body, the oscillatory component decays faster than the averaged component, so that the flow shows there a distinctive steady-state character. This provides a rigorous interpretation of the “steady streaming” phenomenon.

中文翻译：

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通过具有零平均的时间周期运动平移的物体的粘性流

我们研究了 Navier-Stokes 流经过一个物体 $${\mathscr {B}}$$ B 的存在性、唯一性、规律性和渐近空间行为，它以周期 T 的时间周期平移运动移动，并且具有零平均数。例如，$${\mathscr {B}}$$ B 以振荡方式移动。然后我们证明，流动也是具有相同周期 T 的时间周期。然而，离身体足够“远”，振荡分量比平均分量衰减得更快，因此流动在那里显示出独特的稳态特征。这提供了对“稳定流”现象的严格解释。