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On the uniqueness of solutions of the Falkner-Skan equation

Part of: Boundary value problems Incompressible viscous fluids

Published online by Cambridge University Press:  26 February 2010

A. H. Craven  and
L. A. Peletier
A. H. Craven
Affiliation:
University of Sussex, Brighton.
L. A. Peletier
Affiliation:
University of Sussex, Brighton.
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Extract

The study of similarity solutions of Prandtl's equations for the steady two dimensional flow of an incompressible fluid past a rigid wall leads to the equation

where the primes denote differentiation with respect to the independent variable t, and λ is a parameter. It was first obtained in 1930 by Falkner and Skan [3]. For its derivation we refer to Schlichting [6] here we merely note that the function f′(t) represents, after suitable normalization, the velocity parallel to the wall.

MSC classification

Secondary: 34B30: Special equations (Mathieu, Hill, Bessel, etc.) 76D10: Boundary-layer theory, separation and reattachment, higher-order effects
Type
Research Article
Information
Mathematika , Volume 19 , Issue 1 , June 1972 , pp. 129 - 133
Copyright
Copyright © University College London 1972

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References

1.Coppel, W. A., “On a differential equation of boundary layer theory ”, Phil. Trans. Roy. Soc. London, Ser. A, 253 (1960), 101–136.Google Scholar
2.Craven, A. H. and Peletier, L. A., “Reverse flow solutions of the Falkner-Skan equation for λ > 1”, Mathematika, 19(1972), 132–135.Google Scholar
3.Falkner, V. M. and Skan, S. W., “Solutions of the boundary layer equations ”, Phil. Mag., 12 (1931), 865–896.CrossRefGoogle Scholar
4.Hartman, P., Ordinary differential equations (Wiley, New York, 1964).Google Scholar
5.Iglisch, R., “Elementarer Beweis fur die Eindeutigkeit der Stromung in der laminaren Grenzschicht zur Potentialstromung U = u1 xm mit m ≥ = 0 bei Absäugen und Ausblasen ”, Z. Angew. Math. Mech., 34 (1954), 441–443.CrossRefGoogle Scholar
6.Schlichting, H., Boundary Layer Theory, 6th Ed. (McGraw Hill, New York, 1960).Google Scholar
7.Weyl, H., “On the differential equations of the simplest boundary layer problems “, Ann. of Math., 43 (1942), 381–407.CrossRefGoogle Scholar