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Summary:
Yhe problem mentioned in the title is studied with help of the stream function and transformed to the boundary value problem for a quasilinear equation. The existence of the solution is proved and the problem of the uniqueness of the solution is discussed.
References:
[1] R. W. Carrol: Abstract methods in partial differential equations. Harper, Row Publishers, New York, 1968. MR 0433480
[2] M. Feistauer: Some cases of numerical solution of differential equations describing the vortex-flow through three-dimensional axially-symmetric channels. Apl. mat. 16 (1971), No 4, 265-288. MR 0286370 | Zbl 0221.65184
[3] M. Feistauer J. Polášek: The calculation of axially-symmetric stream fields. Proceedings of the Hydro-Turbo Conference 74, Luhačovice 1974 (in Czech).
[4] M. Feistauer: The calculation of some types of stream fields in the model of a unified outlet. Technical research report Tp VZ 11/74, ŠKODA Plzeň, 1974 (in Czech).
[5] O. John J. Nečas: The equations of mathematical physics. SPN Prague, 1972 (in Czech).
[6] J. Nečas: Les méthodes directes en théorie des équations elliptiques. Academia, Prague, 1967. MR 0227584
[7] M. M. Вайнберг: Вариационный метод и метод монотонных операторов. Наука, Москва, 1972. Zbl 1156.34335
[8] И. H. Векуа: Обобщенные аналитические функции. Москва, 1959. Zbl 1047.90504
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