Abstract
The Falkner-Skan equation for similarity solutions of the Prandtl boundary-layer equations for incompressible flow is analysed for both positive and negative values of the parameterβ. Forβ< — 1 branches of solutions with any number of intervals of overshoot are found analytically, and confirm recent numerical results. Forβ> 1 we have proved that there is a periodic solution. We conjecture that forβ> 2 there are infinitely many periodic solutions and that a form of ‘symbolic dynamics’, of the kind associated with a Smale ‘horseshoe map’ can be constructed. We have shown this rigorously forβclose to 2.
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Schedule a callMore From: Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences
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