Proceedings of the Royal Society of Edinburgh: Section A Mathematics

Table of Contents - 1986 - Volume 104, Issue 3-4  

Research Article

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

T. M. Fischera1, G. C. Hsiaoa2 and W. L. Wendlanda3

a1 Institut für Theoretische Strömungsmechanik, DFVLR, D-3400 Göttingen, Federal Republic of Germany

a2 Department of Mathematical Sciences, University of Delaware, Newark, Delaware 19711, U.S.A.

a3 Mathematisches Institut A, Universität Stuttgart, D-7000 Stuttgart 80, Federal Republic of Germany

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.

(Received August 30 1985)

(Revised February 17 1986)

Footnotes

* This research was supported in part by the Alexander-von Humboldt-Stiftung and by the Stiftung Volkswagen werk.