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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
##### Keywords:
existence; energy equation; orientation of particles
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##### References:
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