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Steady-State Navier–Stokes Flows Past a Rotating Body: Leray Solutions are Physically Reasonable

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Abstract

A rigid body, \({\fancyscript{B}}\), moves in a Navier–Stokes liquid, \({\fancyscript{L}}\), filling the whole space outside \({\fancyscript{B}}\). We assume that, when referred to a frame attached to \({\fancyscript{B}}\), the nonzero velocity of the center of mass, ξ, and the angular velocity, ω, of \({\fancyscript{B}}\) are constant and that the flow of \({\fancyscript{L}}\) is steady. Our main theorem implies that every “weak” steady-state solution in the sense of Leray is, in fact, physically reasonable in the sense of Finn, for data of arbitrary “size”. Such a theorem improves and generalizes an analogous famous result of Babenko (Math USSR Sb 20:1–25, 1973), obtained in the case ω = 0.

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Authors and Affiliations

  1. Department of Mechanical Engineering and Materials Science, University of Pittsburgh, Pittsburgh, USA

    Giovanni P. Galdi

  2. Institut für Mathematik, RWTH-Aachen, Aachen, Germany

    Mads Kyed

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  1. Giovanni P. Galdi
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  2. Mads Kyed
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Correspondence to Mads Kyed.

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Communicated by V. Šverák

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Galdi, G.P., Kyed, M. Steady-State Navier–Stokes Flows Past a Rotating Body: Leray Solutions are Physically Reasonable. Arch Rational Mech Anal 200, 21–58 (2011). https://doi.org/10.1007/s00205-010-0350-6

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  • DOI: https://doi.org/10.1007/s00205-010-0350-6

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