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 flow 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 result is based on a thorough study of the pseudodifferential operator relating the normal velocity of the fluid and the normal component of the associated stress tensor along the free surface, and requires the use of the 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. 2011. ⟨hal-00621191v3⟩