[Effets de lissage locaux pour le problème des ondes avec tension superficielle]
Nous considérons le problème des ondes avec une surface libre unidimensionnelle, de profondeur infinie, en utilisant sa formulation comme une équation non linéaire dispersive du second ordre. Nous mettons en évidence un effet de lissage local sous l'influence de la tension superficielle : en moyenne au fil du temps, les solutions acquièrent localement 1/4 de dérivée en plus de la régularité de l'état initial. L'analyse combine des méthodes d'énergie avec des techniques d'opérateurs Fourier intégraux.
The water-wave problem with a one-dimensional free surface of infinite depth is considered, based on the formulation as a second-order nonlinear dispersive equation. The local smoothing effects are established under the influence of surface tension, stating that on average in time solutions acquire locally 1/4 derivative of smoothness as compared to the initial state. The analysis combines energy methods with techniques of Fourier integral operators.
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@article{CRMATH_2009__347_3-4_159_0,
author = {Christianson, Hans and Hur, Vera Mikyoung and Staffilani, Gigliola},
title = {Local smoothing effects for the water-wave problem with surface tension},
journal = {Comptes Rendus. Math\'ematique},
pages = {159--162},
publisher = {Elsevier},
volume = {347},
number = {3-4},
year = {2009},
doi = {10.1016/j.crma.2008.12.010},
language = {en},
url = {http://archive.numdam.org/articles/10.1016/j.crma.2008.12.010/}
}
TY - JOUR AU - Christianson, Hans AU - Hur, Vera Mikyoung AU - Staffilani, Gigliola TI - Local smoothing effects for the water-wave problem with surface tension JO - Comptes Rendus. Mathématique PY - 2009 SP - 159 EP - 162 VL - 347 IS - 3-4 PB - Elsevier UR - http://archive.numdam.org/articles/10.1016/j.crma.2008.12.010/ DO - 10.1016/j.crma.2008.12.010 LA - en ID - CRMATH_2009__347_3-4_159_0 ER -
%0 Journal Article %A Christianson, Hans %A Hur, Vera Mikyoung %A Staffilani, Gigliola %T Local smoothing effects for the water-wave problem with surface tension %J Comptes Rendus. Mathématique %D 2009 %P 159-162 %V 347 %N 3-4 %I Elsevier %U http://archive.numdam.org/articles/10.1016/j.crma.2008.12.010/ %R 10.1016/j.crma.2008.12.010 %G en %F CRMATH_2009__347_3-4_159_0
Christianson, Hans; Hur, Vera Mikyoung; Staffilani, Gigliola. Local smoothing effects for the water-wave problem with surface tension. Comptes Rendus. Mathématique, Tome 347 (2009) no. 3-4, pp. 159-162. doi : 10.1016/j.crma.2008.12.010. http://archive.numdam.org/articles/10.1016/j.crma.2008.12.010/
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