Advances in Differential Equations

On the Blasius problem

Bernard Brighi, Augustin Fruchard, and Tewfik Sari

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The Blasius problem $f'''+ff''=0$, $f(0)=-a$, $f'(0)=b$, $f'(+\infty)={\lambda}$ is exhaustively investigated. In particular, the difficult and scarcely studied case $b <0\leq{\lambda}$ is analyzed in details, in which the shape and the number of solutions is determined. The method is first, to reduce to the Crocco equation $uu''+s=0$, and then to use an associated autonomous planar vector field. The most useful properties of Crocco solutions appear to be related to canard solutions of a slow fast vector field.

Article information

Adv. Differential Equations, Volume 13, Number 5-6 (2008), 509-600.

First available in Project Euclid: 18 December 2012

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 34B15: Nonlinear boundary value problems
Secondary: 34B40: Boundary value problems on infinite intervals 76D10: Boundary-layer theory, separation and reattachment, higher-order effects


Brighi, Bernard; Fruchard, Augustin; Sari, Tewfik. On the Blasius problem. Adv. Differential Equations 13 (2008), no. 5-6, 509--600.

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