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Keywords:
flow of plane vector field around boundary of region; conformal mappings
flow of plane vector field around boundary of region; conformal mappings
Summary:
Two well known definitions of the flow of a plane vector field around the boundary of a region $\Omega$ are compared. The definition (appropriately arranged) based on the constantness of the stream function on every profile is not only invariant under conformal mappings but more general than the definition based on the vanishing of the normal component of the field on $\partial \Omega$.
References:
[1] R. B. Burckel: An Introduction to Classical Complex Analysis. Birkhäuser Verlag, Basel und Stuttgart, 1979. Zbl 0434.30002
[2] Г. M. Голузин: Геометрическая теория функций комплексного переменного. Москва-Ленинград, 1952. Zbl 1145.11324
[3] K. Kuratowski: Topologie II. Warszawa, 1952.
[4] S. Saks A. Zygmund: Analytic Functions. Warszawa-Wroclaw, 1952. MR 0055432
[5] I. Černý: Analysis in the Complex Domain. (Czech, to appear in 1983). MR 0729313
[6] I. Černý: Fundaments of Analysis in the Complex Domain. (Czech), Praha 1967.
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