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On two-dimensional slow viscous flows past obstacles in a half-plane*

Published online by Cambridge University Press:  14 November 2011

T. M. Fischer ,
G. C. Hsiao  and
W. L. Wendland
T. M. Fischer
Affiliation:
Institut für Theoretische Strömungsmechanik, DFVLR, D-3400 Göttingen, Federal Republic of Germany
G. C. Hsiao
Affiliation:
Department of Mathematical Sciences, University of Delaware, Newark, Delaware 19711, U.S.A.
W. L. Wendland
Affiliation:
Mathematisches Institut A, Universität Stuttgart, D-7000 Stuttgart 80, Federal Republic of Germany
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Synopsis

We consider a cylinder with arbitrary cross section moving in a viscous incompressible fluid parallel to a plane wall. Formal asymptotic expansions of the solution for small Reynolds numbers are constructed by using boundary integral equations of the first kind. In contrast to the problem without a wall, we show that there exists a unique solution to the zeroth order problem. However, the problem considered here is still singular in the sense that we find the Stokes paradox in the next higher order problem. A justification of the formal asymptotic expansion for the first two terms is established rigorously.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 104 , Issue 3-4 , 1986 , pp. 205 - 215
Copyright
Copyright © Royal Society of Edinburgh 1986

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