Singular problem for a third-order nonlinear ordinary differential equation arising in fluid dynamics

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.