On the Blasius Problem
Résumé
The Blasius problem $f'''+ff''=0$ on $[0,+\infty[$, $f(0)=-a, f'(0)=b, f'(+\infty)=\l$ is exhaustively investigated. In particular the difficult and scarcely studied case $b<0\leq\l$ 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 $u''=-\frac su$ 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.
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