On a mapping property of the Oseen operator with rotation

Mads Kyed

doi:10.3934/dcdss.2013.6.1315

Article Contents

2013, Volume 6, Issue 5: 1315-1322. Doi: 10.3934/dcdss.2013.6.1315

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On a mapping property of the Oseen operator with rotation

Mads Kyed^1,

1.
Fachbereich Mathematik, Technische Universität Darmstadt, Schlossgartenstr. 7, 64289 Darmstadt

Received: July 31, 2011

Revised: October 31, 2011

Published: September 2013

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Abstract

The Oseen problem arises as the linearization of a steady-state Navier-Stokes flow past a translating body. If the body, in addition to the translational motion, is also rotating, the corresponding linearization of the equations of motion, written in a frame attached to the body, yields the Oseen system with extra terms in the momentum equation due to the rotation. In this paper, the effect these rotation terms have on the asymptotic structure at spatial infinity of a solution to the system is studied. A mapping property of the whole space Oseen operator with rotation is identified from which asymptotic properties of a solution can be derived. As an application, an asymptotic expansion of a steady-state, linearized Navier-Stokes flow past a rotating and translating body is established.

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Mathematics Subject Classification: Primary: 35Q30; Secondary: 35B40, 35C20, 76D05.

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References

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