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September/October 2012 Stationary free surface viscous flows without surface tension in three dimensions
Frederic Abergel, Jacques-Herbert Bailly
Differential Integral Equations 25(9/10): 801-820 (September/October 2012). DOI: 10.57262/die/1356012369


We consider an incompressible, viscous, finite depth fluid flowing 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 linearized problem, particularly 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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Frederic Abergel. Jacques-Herbert Bailly. "Stationary free surface viscous flows without surface tension in three dimensions." Differential Integral Equations 25 (9/10) 801 - 820, September/October 2012.


Published: September/October 2012
First available in Project Euclid: 20 December 2012

zbMATH: 1274.35279
MathSciNet: MR2985681
Digital Object Identifier: 10.57262/die/1356012369

Primary: 35R35 , 35S05 , 76D05

Rights: Copyright © 2012 Khayyam Publishing, Inc.

Vol.25 • No. 9/10 • September/October 2012
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