Stationary free surface viscous flows without surface tension in three dimensions

Frédéric Abergel (1) , Jacques-Herbert Bailly (2)

1 MAS - Mathématiques Appliquées aux Systèmes - EA 4037
2 LM-Orsay - Laboratoire de Mathématiques d'Orsay

We consider an incompressible, viscous free surface fl ow down a three dimensional channel. In the absence of surface tension, we prove the existence of a unique stationary solution in weighted Sobolev spaces. The proof relies on a careful study of a particular pseudodifferential operator and the use of a Nash-Moser implicit function theorem.

Domaines: Equations aux dérivées partielles [math.AP]

Frédéric Abergel, Jacques-Herbert Bailly. Stationary free surface viscous flows without surface tension in three dimensions. 1999. ⟨hal-00621191v1⟩