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The steady motion of a Navier-Stokes liquid around a rigid body. (English) Zbl 1111.76010
Summary: 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 R. Finn [ibid. 19, 363–406 (1965; Zbl 0149.44606)]. In particular, they are unique and satisfy the energy equation. Among other things, this result is relevant to engineering applications involving orientation of particles in viscous liquid.

MSC:
76D03 Existence, uniqueness, and regularity theory for incompressible viscous fluids
35Q30 Navier-Stokes equations
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