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On the non-existence of periodic neutral-wave solutions to a complex-valued periodic differential equation

Part of: Incompressible viscous fluids

Published online by Cambridge University Press:  26 February 2010

A. G. Walton
A. G. Walton
Affiliation:
Department of Mathematics, Imperial College of Science, Technology & Medicine, 180 Queen's Gate, London SW7 2BZ.
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Abstract

The equation

where ℱ is a certain complex-valued function of the given real periodic function λ, is studied analytically and numerically. The equation is motivated physically by a boundary-layer stability problem in which λ represents the skin-friction of the undisturbed basic flow profile. It is proved that no periodic neutral solutions exist for any attached basic flow and the implications of this result for certain vortex-wave interactions are discussed.

MSC classification

Secondary: 76D10: Boundary-layer theory, separation and reattachment, higher-order effects
Type
Research Article
Information
Mathematika , Volume 43 , Issue 2 , December 1996 , pp. 371 - 381
Copyright
Copyright © University College London 1996

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