Geodesic
Singular problem for a third-order nonlinear ordinary differential equation arising in fluid dynamics
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 47 (2007) no. 7, pp. 1158-1178

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Results concerning singular Cauchy problems, smooth manifolds, and Lyapunov series are used to correctly state and analyze a singular “initial-boundary” problem for a third-order nonlinear ordinary differential equation defined on the entire real axis. This problem arises in viscous incompressible fluid dynamics and describes self-similar solutions to the boundary layer equation for the stream function with a zero pressure gradient (plane-parallel flow in a mixing layer). The analysis of the problem suggests a simple numerical method for its solution. Numerical results are presented. 
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A. L. Duischko; N. B. Konyukhova; A. I. Sukov. Singular problem for a third-order nonlinear ordinary differential equation arising in fluid dynamics. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 47 (2007) no. 7, pp. 1158-1178. http://geodesic.mathdoc.fr/item/ZVMMF_2007_47_7_a3/