[Sur l'existence et la stabilité des ondes solitaires en présence d'une faible tension superficielle]
Récemment, Buffoni (2005, 2009) [2,3] a développé une théorie d'existence et de stabilité des ondes solitaires de surface dans le cas d'une faible tension de surface. Cette théorie, qui est de nature variationnelle, repose sur l'hypothèse que l'infimum d'une certaine fonctionnelle variationnelle est strictement sous-homogène par rapport à un petit paramètre. Dans cette Note, on démontre cette propriété de sous-homogénéité stricte complétant ansi la théorie de Buffoni.
An existence and stability theory for solitary water waves with weak surface tension has recently been given by Buffoni (2005, 2009) [2,3]. The theory, which is variational in nature, relies upon the assumption that the infimum of the variational functional is strictly subhomogeneous with respect to a small parameter. In this Note we rigorously establish the relevant strict-subhomogeneity property and thus complete Buffoni's theory.
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@article{CRMATH_2010__348_7-8_397_0,
author = {Groves, Mark D. and Wahl\'en, E.},
title = {On the existence and conditional energetic stability of solitary water waves with weak surface tension},
journal = {Comptes Rendus. Math\'ematique},
pages = {397--402},
publisher = {Elsevier},
volume = {348},
number = {7-8},
year = {2010},
doi = {10.1016/j.crma.2010.01.003},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2010.01.003/}
}
TY - JOUR AU - Groves, Mark D. AU - Wahlén, E. TI - On the existence and conditional energetic stability of solitary water waves with weak surface tension JO - Comptes Rendus. Mathématique PY - 2010 SP - 397 EP - 402 VL - 348 IS - 7-8 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2010.01.003/ DO - 10.1016/j.crma.2010.01.003 LA - en ID - CRMATH_2010__348_7-8_397_0 ER -
%0 Journal Article %A Groves, Mark D. %A Wahlén, E. %T On the existence and conditional energetic stability of solitary water waves with weak surface tension %J Comptes Rendus. Mathématique %D 2010 %P 397-402 %V 348 %N 7-8 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2010.01.003/ %R 10.1016/j.crma.2010.01.003 %G en %F CRMATH_2010__348_7-8_397_0
Groves, Mark D.; Wahlén, E. On the existence and conditional energetic stability of solitary water waves with weak surface tension. Comptes Rendus. Mathématique, Tome 348 (2010) no. 7-8, pp. 397-402. doi : 10.1016/j.crma.2010.01.003. http://www.numdam.org/articles/10.1016/j.crma.2010.01.003/
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