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Exponential Decay of the Vorticity in the Steady-State Flow of a Viscous Liquid Past a Rotating Body

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Abstract

Consider the flow of a Navier–Stokes liquid past a body rotating with a prescribed constant angular velocity, \({\omega}\), and assume that the motion is steady with respect to a body-fixed frame. In this paper we show that the vorticity field associated to every “weak” solution corresponding to data of arbitrary “size” (Leray Solution) must decay exponentially fast outside the wake region at sufficiently large distances from the body. Our result improves and generalizes in a non-trivial way famous results by Clark (Indiana Univ Math J 20:633–654, 1971) and Babenko and Vasil’ev (J Appl Math Mech 37:651–665, 1973) obtained in the case \({\omega=0}\).

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Authors and Affiliations

  1. EA 2797 - LMPA - Laboratoire de mathématiques pures et appliquées Joseph Liouville, Univ. Littoral Côte d’Opale, 62228, Calais, France

    Paul Deuring

  2. Department of Mechanical Engineering and Materials Science, University of Pittsburgh, 3700 O’Hara Street, Pittsburgh, PA, 15261, USA

    Giovanni P. Galdi

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  1. Paul Deuring
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  2. Giovanni P. Galdi
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Correspondence to Paul Deuring.

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Communicated by V. Šverák

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Deuring, P., Galdi, G.P. Exponential Decay of the Vorticity in the Steady-State Flow of a Viscous Liquid Past a Rotating Body. Arch Rational Mech Anal 221, 183–213 (2016). https://doi.org/10.1007/s00205-015-0959-6

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