Tuen-Wai Ng, HKU, Hong Kong

Exact Meromorphic Solutions of the Falkner-Skan Differential Equation

 

Abstract

In this talk, we shall apply a method first developed by A. Eremenko to find the exact solutions of some interesting non-linear autonomous differential equations including the Falkner-Skan differential equation

f''' + ff'' + b(1 - f '2) = 0 .

This third order O.D.E describes the boundary-layer flow over a wedge of included angle bp and it has been studied intensively in fluid mechanics. The solution f, if it exists, is called the shape function, or the dimensionless stream function and its first derivative, after suitable normalization, represents the velocity.