[Cosymétrie équivariante et solutions « fronts » de l'équation de Dubreil–Jacotin–Long. 2ème partie : Solutions exactes]
Cette Note traite de l'existence de solutions exactes de l'équation de Dubreil–Jacotin–Long (DJL), qui décrivent les fronts internes de grande amplitude dans un fluide continûment stratifié. La démonstration utilise une variante du théorème des fonctions implicites en présence d'une cosymétrie, basée sur le groupe d'invariance de la fonctionnelle variationnelle de l'opérateur de DJL. Une bifurcation supercritique a lieu au bord du spectre continu du problème linéarisé au voisinage de l'écoulement primaire.
The paper concerns existence of exact solutions of the Dubreil–Jacotin–Long equation describing large amplitude internal fronts in a continuously stratified fluid. The proof uses cosymmetric variant of the implicit function theorem based on the group invariance of the variational functional for DJL operator. Supercritical branching occurs near approximate front solutions at the boundary of continuous spectrum of the problem linearized with respect to the basic uniform flow.
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@article{CRMATH_2003__337_12_815_0,
author = {Makarenko, Nikolai},
title = {Equivariant cosymmetry and front solutions of the {Dubreil{\textendash}Jacotin{\textendash}Long} equation. {Part} 2: {Exact} solutions},
journal = {Comptes Rendus. Math\'ematique},
pages = {815--818},
publisher = {Elsevier},
volume = {337},
number = {12},
year = {2003},
doi = {10.1016/j.crma.2003.09.036},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2003.09.036/}
}
TY - JOUR AU - Makarenko, Nikolai TI - Equivariant cosymmetry and front solutions of the Dubreil–Jacotin–Long equation. Part 2: Exact solutions JO - Comptes Rendus. Mathématique PY - 2003 SP - 815 EP - 818 VL - 337 IS - 12 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2003.09.036/ DO - 10.1016/j.crma.2003.09.036 LA - en ID - CRMATH_2003__337_12_815_0 ER -
%0 Journal Article %A Makarenko, Nikolai %T Equivariant cosymmetry and front solutions of the Dubreil–Jacotin–Long equation. Part 2: Exact solutions %J Comptes Rendus. Mathématique %D 2003 %P 815-818 %V 337 %N 12 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2003.09.036/ %R 10.1016/j.crma.2003.09.036 %G en %F CRMATH_2003__337_12_815_0
Makarenko, Nikolai. Equivariant cosymmetry and front solutions of the Dubreil–Jacotin–Long equation. Part 2: Exact solutions. Comptes Rendus. Mathématique, Tome 337 (2003) no. 12, pp. 815-818. doi : 10.1016/j.crma.2003.09.036. http://www.numdam.org/articles/10.1016/j.crma.2003.09.036/
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