Sfb 288 Differential Geometry and Quantum Physics

Abstract for Sfb Preprint No. 491

Conformal Reparametrization of a Free Boundary Flow in 2D Hydrodynamics

W. Klingenberg and J. Stalker

We study a 2D potential flow problem with both free and prescribed boundary conditions. A conformal reparametrization of the domain of the flow leads to a first order elliptic system with first order boundary conditions for the flow and the parametrization. We prove that this system in elliptic and give its index. The index computation uses properties of the Atiyah-Bott formula and index formulae for the classical Riemann-Hilbert boundary problem. In the case of the centrifuge with an annulus-type profile, we prove that the system admits a one dimensional kernel and cokernel.

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