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