Journal ArticleDOI
Large-time existence of surface waves in incompressible viscous fluids with or without surface tension
Atusi Tani,Naoto Tanaka +1 more
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This article is published in Archive for Rational Mechanics and Analysis.The article was published on 1995-12-01. It has received 131 citations till now. The article focuses on the topics: Free surface & Surface tension.read more
Citations
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Journal ArticleDOI
Almost Exponential Decay of Periodic Viscous Surface Waves without Surface Tension
TL;DR: Guo et al. as mentioned in this paper considered a viscous fluid of finite depth below the air, occupying a three-dimensional domain bounded below by a fixed solid boundary and above by a free moving boundary.
Journal ArticleDOI
On the two-phase navier-stokes equations with surface tension
Gottfried Anger,Gieri Simonett +1 more
TL;DR: In this paper, the Navier-Stokes free boundary problem is considered in a situation where the initial interface is close to a halfplane and the fluids are separated by an interface that is unknown and has to be determined as part of the problem.
Journal ArticleDOI
Local well-posedness of the viscous surface wave problem without surface tension
TL;DR: In this paper, the authors consider a viscous fluid of finite depth below the air, occupying a three-dimensional domain bounded below by a fixed solid boundary and above by a free moving boundary.
Journal ArticleDOI
Small-time existence for the three-dimensional navier-stokes equations for an incompressible fluid with a free surface
TL;DR: In this paper, the authors considered the problem of describing the motion of a layer of heavy, viscous, incompressible fluid lying above an infinite rigid bottom and having a non-compact free surface with no surface tension.
Posted Content
Decay of viscous surface waves without surface tension
TL;DR: In this paper, a local well-posedness theory of the Navier-Stokes equations in the presence of a moving boundary and a two-tier energy method were proposed to solve the long time behavior of a free surface with small amplitude.
References
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Journal ArticleDOI
Large-time regularity of viscous surface waves
TL;DR: Etude du mouvement d'un fluide visqueux incompressible contenu dans un ocean tridimensionnel de dimensions finies, limite en bas par un sol solide et en haut par une atmosphere a pression constant as discussed by the authors.
Book ChapterDOI
Large-Time Behavior of Viscous Surface Waves.
J. T. Beale,Takaaki Nishida +1 more
TL;DR: In this paper, the large-time behavior of viscous surface waves is discussed and global in time solutions to a free surface problem of the viscous incompressible fluid, which is formulated as the motion of the fluid, governed by the Navier-Stokes equation, are presented.
Journal ArticleDOI
On the transient motion of an isolated volume of viscous incompressible fluid
TL;DR: In this paper, it was shown that the free-boundary problem of describing the evolution of a viscous incompressible fluid in time without taking surface tension into account is solvable locally in time and sufficient conditions for the extension of a solution to the infinite time interval were given.
Journal ArticleDOI
Large time existence of small viscous surface waves without surface tension
Donna Lynn,Gates Sylvester +1 more
TL;DR: In this article, the authors studied the case where the fluid is in an ocean of infinite extent and finite depth with the Navier-Stokes equations, and they showed that the motion of a viscous, imcompressible fluid is governed by these equations.