[Sur la structure hamiltonienne du problème des ondes de surface planes stationnaires avec vorticité]
Nous considérons la formulation de la fonction du courant dans le problème hydrodynamique décrivant les ondes de surface rotationnelles stationnaires, avec ou sans tension superficielle. Dans les deux cas, nous présentons une formulation lagrangienne naturelle, à partir de laquelle (différentes) formulations hamiltoniennes sont dérivées à l'aide de la théorie de la dualité, dans l'esprit de la transformée de Legendre–Fenchel. La démarche est systématique et clarifie une approche ad hoc récente de Kozlov et Kuznetsov [7].
We consider the stream-function formulation of the hydrodynamic problem for steady rotational water waves both with and without surface tension. A natural Lagrangian formulation is presented from which (different) Hamiltonian formulations for the two cases are derived by duality theory in the spirit of the Legendre–Fenchel transform. The treatment is systematic and clarifies a recent ad hoc approach by Kozlov and Kuznetsov [7].
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@article{CRMATH_2014__352_3_205_0,
author = {Groves, Mark D. and Stylianou, Athanasios},
title = {On the {Hamiltonian} structure of the planar steady water-wave problem with vorticity},
journal = {Comptes Rendus. Math\'ematique},
pages = {205--211},
publisher = {Elsevier},
volume = {352},
number = {3},
year = {2014},
doi = {10.1016/j.crma.2014.01.006},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2014.01.006/}
}
TY - JOUR AU - Groves, Mark D. AU - Stylianou, Athanasios TI - On the Hamiltonian structure of the planar steady water-wave problem with vorticity JO - Comptes Rendus. Mathématique PY - 2014 SP - 205 EP - 211 VL - 352 IS - 3 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2014.01.006/ DO - 10.1016/j.crma.2014.01.006 LA - en ID - CRMATH_2014__352_3_205_0 ER -
%0 Journal Article %A Groves, Mark D. %A Stylianou, Athanasios %T On the Hamiltonian structure of the planar steady water-wave problem with vorticity %J Comptes Rendus. Mathématique %D 2014 %P 205-211 %V 352 %N 3 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2014.01.006/ %R 10.1016/j.crma.2014.01.006 %G en %F CRMATH_2014__352_3_205_0
Groves, Mark D.; Stylianou, Athanasios. On the Hamiltonian structure of the planar steady water-wave problem with vorticity. Comptes Rendus. Mathématique, Tome 352 (2014) no. 3, pp. 205-211. doi : 10.1016/j.crma.2014.01.006. http://www.numdam.org/articles/10.1016/j.crma.2014.01.006/
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