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Asymptotic structure
of a Leray solution to the Navier–Stokes flow around a
rotating body
Reinhard Farwig, Giovanni P. Galdi and Mads Kyed |
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Vol. 253 (2011), No. 2, 367–382
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Abstract |
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Consider a body, ℬ, rotating with constant angular velocity ω and fully submerged in a Navier–Stokes liquid that fills the whole space exterior to ℬ. We analyze the flow of the liquid that is steady with respect to a frame attached to ℬ. Our main theorem shows that the velocity field v of any weak solution (v,p) in the sense of Leray has an asymptotic expansion with a suitable Landau solution as leading term and a remainder decaying pointwise like 1∕|x|1+α as |x|→∞ for any α ∈ (0,1), provided the magnitude of ω is below a positive constant depending on α. We also furnish analogous expansions for ∇v and for the corresponding pressure field p. These results improve and clarify a recent result of R. Farwig and T. Hishida. |
Keywords
Navier–Stokes equations, asymptotic behavior of solutions,
rotating frame
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Mathematical Subject Classification 2010
Primary: 35B40, 35Q30, 76U05, 76D05
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Milestones
Received: 30 September 2010
Revised: 13 March 2011
Accepted: 15 March 2011
Published: 21 January 2012
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Authors |
| Reinhard Farwig | |
| Fachbereich Mathematik and Center of
Smart Interfaces (CSI) Technische Universität Darmstadt D-64289 Darmstadt Germany |
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| Giovanni P. Galdi | |
| Department of Mechanical Engineering
and Materials Science University of Pittsburgh Pittsburgh PA 15261 United States |
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| Mads Kyed | |
| Fachbereich Mathematik Technische Universität Darmstadt Schlossgartenstrasse 7 D-64289 Darmstadt Germany |
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