The FENE model for viscoelastic thin film flows: Justification of new models and applications.

Laurent Chupin (1)

1 ICJ - Institut Camille Jordan

In this article, we rigorously determine an asymptotic model for viscoelastic flows of FENE type for thin domains. The proof presented here is based on existence and unicity results for a Fokker-Planck equation and for the limit problem when the ratio between height and width of the physical domain vanished. We finally show that the error between complete FENE constitutive law and the approximation suggested for thin films domains can be controlled. Some applications are given at the end of this article: in the fields of lubrication, phenomena of boundary layers, of the industry of the nanotechnology, of biology or Shallow-Water equations.

Domaines: Equations aux dérivées partielles [math.AP]; Physique mathématique [math-ph]; Physique mathématique [math-ph]

Laurent Chupin. The FENE model for viscoelastic thin film flows: Justification of new models and applications.. 2008. ⟨hal-00270113⟩