Lyapunov stability of solitary rotational water waves
作者:
V. Artale,
E. Salusti,
R. Santoleri,
期刊:
Geophysical & Astrophysical Fluid Dynamics
(Taylor Available online 1986)
卷期:
Volume 37,
issue 3
页码: 237-251
ISSN:0309-1929
年代: 1986
DOI:10.1080/03091928608210098
出版商: Taylor & Francis Group
关键词: Euler equation;Lyapunov stability;solitary waves
数据来源: Taylor
摘要:
Generalizing an idea of Arnold, we discuss the hydrodynamic stability à la Lyapunov of solitary water-waves which are rotational solutions of the Euler equation, travelling with constant phase speed[ctilde]T. In the reference frame moving with the wave profile, the solitary wave is described by a solution ofWe show that ifas in other applications of Arnold's idea, and ifat the air sea surface, a rather realistic request, the system is stable for (a) small vertical or horizontal space scale perturbations; (b) perturbations with a very long vertical space scale and very small horizontal space scale or with a very long horizontal space scale and very small vertical space scale. Finally we show that the system is also stable for irrotational perturbations.
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