The Blasius equation

Augustin Fruchard (1) , Bernard Brighi (1) , Tewfik Sari (1, 2)

1 LMIA - Laboratoire de Mathématiques Informatique et Applications [UHA]
2 MISTEA - Mathématiques, Informatique et STatistique pour l'Environnement et l'Agronomie

The Blasius problem f'''+ff''=0, f(0)=-a, f'(0)=b, f'(infinity)=lambda is investigated, in particular in the difficult and scarcely studied case b<0<=lambda. The shape and the number of solutions are 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.

Mots clés: Blasius equation; Crocco equation boundary value problem on infinite interval; Canard solution

Domaines: Mathématiques générales [math.GM]

Augustin Fruchard, Bernard Brighi, Tewfik Sari. The Blasius equation. 2010. ⟨hal-00493860⟩