The Steady Motion of a Navier–Stokes Liquid Around a Rigid Body
The Steady Motion of a Navier–Stokes Liquid Around a Rigid Body
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纳维的稳定运动——在刚体周围激起液体
DOI：
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发表时间：
2007
期刊：
影响因子：
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通讯作者：
A. Silvestre
中科院分区：
文献类型：
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作者：
G. Galdi;A. Silvestre
设$${\Mathcal{R}}$$是在充满整个空间的N-S液体中按规定的刚性运动运动的物体，它受给定的边界条件和体力的约束。在假设对于附加在$${\mathcal{R}}$$上的帧$${\mathcal{F}}$$，这些数据是时间无关的，并且它们的大小不是“太大”的情况下，我们证明了关于$${\mathcal{F}}$$存在且只有一个相应的稳定运动$$\mathcal{L}$$，使得空间中一般点x处的速度场像|x|−1一样衰减。这些解在Finn[10]的意义下是“物理上合理的”。特别是，它们是唯一的，并且满足能量方程。此外，这一结果还适用于涉及粘性液体中颗粒取向的工程应用[14]。
Let $${\mathcal {R}}$$ be a body moving by prescribed rigid motion in a Navier–Stokes liquid $${\mathcal {L}}$$ that fills the whole space and is subject to given boundary conditions and body force. Under the assumptions that, with respect to a frame $${\mathcal {F}}$$ , attached to $${\mathcal {R}}$$ , these data are time independent, and that their magnitude is not “too large”, we show the existence of one and only one corresponding steady motion of $${\mathcal {L}}$$ , with respect to $${\mathcal {F}}$$ , such that the velocity field, at the generic point x in space, decays like |x|−1. These solutions are “physically reasonable” in the sense of FINN [10]. In particular, they are unique and satisfy the energy equation. Among other things, this result is relevant in engineering applications involving orientation of particles in viscous liquid [14].