Differential and Integral Equations

Stationary free surface viscous flows without surface tension in three dimensions

Frederic Abergel and Jacques-Herbert Bailly

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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.

Article information

Differential Integral Equations, Volume 25, Number 9/10 (2012), 801-820.

First available in Project Euclid: 20 December 2012

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35R35: Free boundary problems 76D05: Navier-Stokes equations [See also 35Q30] 35S05: Pseudodifferential operators


Abergel, Frederic; Bailly, Jacques-Herbert. Stationary free surface viscous flows without surface tension in three dimensions. Differential Integral Equations 25 (2012), no. 9/10, 801--820. https://projecteuclid.org/euclid.die/1356012369

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