Author: W. Balser 1
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  • 1 Abteilungen Mathematik I und V Universität ULM 89 069 ULM Germany
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We study solutions of Stokes' equation in a regionD (in the complex plane) being the intersection of a sector with vertex at the origin and a ring about the origin, subject to no-slip boundary conditions on the radial boundaries ofD. Using a result of Kratz and Peyerimhoff, we represent solutionsv(z) by means of two analytic functionsv1(z) andv2(z), and for these we obtain expansions into infinite series, quite analogous to Laurent series, but in complex powers ofz, the exponents depending upon the angular opening ofD. Forv(z), this leads to an expansion quite analogous to the one stated without proof by Moffat in 1964 in a more special situation.