Article Dans Une Revue Differential and integral equations Année : 2012

Stationary free surface viscous flows without surface tension in three dimensions

Résumé

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.

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Dates et versions

hal-00621191 , version 1 (09-09-2011)
hal-00621191 , version 2 (28-09-2011)
hal-00621191 , version 3 (04-11-2011)
hal-00621191 , version 4 (22-11-2011)
hal-00621191 , version 5 (31-12-2011)
hal-00621191 , version 6 (04-01-2012)
hal-00621191 , version 7 (14-01-2012)

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  • HAL Id : hal-00621191 , version 7

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Frédéric Abergel, Jacques-Herbert Bailly. Stationary free surface viscous flows without surface tension in three dimensions. Differential and integral equations, 2012, 25 (9-10), pp.801-820. ⟨hal-00621191v7⟩
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