Viscoelastic flows in a rough channel: a multiscale analysis

Laurent Chupin (1) , Sébastien Martin (2)

1 LMBP - Laboratoire de Mathématiques Blaise Pascal
2 MAP5 - UMR 8145 - Mathématiques Appliquées Paris 5

In this paper, we consider viscoelastic flows in a rough domain (with typical roughness patterns of size ε ≪ 1). We present and rigorously justify an asymptotic expansion with respect to ε, at any order, based upon the definition of elementary problems: Oldroyd-type problems at the global scale defined on a smoothened domain and boundary-layer corrector problems. The resulting analysis guarantees optimality with respect to the truncation error.

Domaines: Equations aux dérivées partielles [math.AP]

Laurent Chupin, Sébastien Martin. Viscoelastic flows in a rough channel: a multiscale analysis. Annales de l'Institut Henri Poincaré C, Analyse non linéaire, 2016. ⟨hal-01129984⟩