The Blasius equation

B. Brighi (1) , A. Fruchard (1) , T. Sari (2)

1 LMIA - Laboratoire de Mathématiques Informatique et Applications [UHA]
2 UMR ITAP - Information – Technologies – Analyse Environnementale – Procédés Agricoles

The Blasius problem f′′′ + ff′′ = 0, f(0) = −a, f′(0) = b, f′(+\infty)=\lambda is investigated, in particular in the difficult and scarcely studied case b < 0 \leq \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: EQUATION; FONCTION MATHEMATIQUE; BLASIUS EQUATION; CROCCO EQUATION; BOUNDARY VALUE PROBLEM ON INFINITE INTERVAL; CANARD SOLUTION

Domaines: Sciences de l'environnement

B. Brighi, A. Fruchard, T. Sari. The Blasius equation. Colloque à la mémoire d’Emmanuel Isambert, Université de Paris 7, Dec 2007, Paris, France. p. 105 - p. 123. ⟨hal-00765316⟩