Inertial effects in the asymptotic behavior of a thin film flow

Article type: Research Article

Authors: Assemien, Ahiko^; | Bayada, Guy | Chambat, Michèle

Affiliations: Université Lyon I, Laboratoire d'Analyse Numérique, URA 740 CNRS, Bât. 101, 69622 Villeurbanne Cedex, France | I.N.S.A., URA 856 et URA 740 CNRS, Centre de Mathématiques, Bât. 401, 69621 Villeurbanne Cedex, France

Abstract: We study the dependence with respect to the domain of the constants appearing in some Sobolev embeddings. It shows that the inertial effects are negligible at the first order for the asymptotic behavior of a thin film flow. The influence of the inertial effects is obtained at the second order in the asymptotic expansions of the pressure and velocity, with full convergence argument for chosen boundary conditions.

DOI: 10.3233/ASY-1994-9301

Journal: Asymptotic Analysis, vol. 9, no. 3, pp. 177-208, 1994