On the Blasius Problem

Bernard Brighi (1) , Augustin Fruchard (1) , Tewfik Sari (1)

1 LMIA - Laboratoire de Mathématiques Informatique et Applications [UHA]

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.

Mots clés: Blasius equation; Crocco equation; boundary value problem on infinite interval; canard solution; ordinary differential equation

Domaines: Systèmes dynamiques [math.DS]

Bernard Brighi, Augustin Fruchard, Tewfik Sari. On the Blasius Problem. 2008. ⟨hal-00114834v2⟩