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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.

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