Non–existence of solitary water waves in three dimensions

In the subject of free-surface water waves, solitary waves play an important role in the theory of two-dimensional fluid motions. These are steady solutions to the Euler equations that are localized, positively elevated above the mean fluid level and travelling at velocities with supercritical Froud...

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Bibliographic Details
Published in:Philosophical transactions of the Royal Society of London. Series A: Mathematical, physical, and engineering sciences physical, and engineering sciences, 2002-10, Vol.360 (1799), p.2127-2135
Main Author: Craig, Walter
Format: Article
Language:English
Subjects:
A priori knowledge
Boundary conditions
Extrema
Fluid Dynamics
Infinity
Mathematical minima
Mathematics
Models, Theoretical
Motion
Phase velocity
Rheology - methods
Solitary Waves
Solitons
Surface Properties
Water
Water Movements
Water Waves
Waves
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Summary:In the subject of free-surface water waves, solitary waves play an important role in the theory of two-dimensional fluid motions. These are steady solutions to the Euler equations that are localized, positively elevated above the mean fluid level and travelling at velocities with supercritical Froude number. They provide a stable mechanism in bodies of water for transport of mass, momentum and energy over long distances. In this paper, we prove that in the three- (or higher-) dimensional problem of surface water waves, there do not exist any localized steady positive solutions to the Euler equations.
ISSN:1364-503X
1471-2962
DOI:10.1098/rsta.2002.1065