L’équation de KdV est considérée comme un modèle approximatif pour des ondes longues de faible amplitude à la surface libre d’un fluide non visqueux. On montre qu’il y a une densité de moment approximative associée à l’équation de KdV, et que la différence entre cette densité et la densité de de moment physique dérivée dans le contexte du système d’Euler peut être estimée en fonction du paramètre d’onde longue.
Consideration is given to the KdV equation as an approximate model for long waves of small amplitude at the free surface of an inviscid fluid. It is shown that there is an approximate momentum density associated to the KdV equation, and the difference between this density and the physical momentum density derived in the context of the full Euler equations can be estimated in terms of the long-wave parameter.
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@article{CRMATH_2021__359_1_39_0,
author = {Israwi, Samer and Kalisch, Henrik},
title = {A {Mathematical} {Justification} of the {Momentum} {Density} {Function} {Associated} to the {KdV} {Equation}},
journal = {Comptes Rendus. Math\'ematique},
pages = {39--45},
publisher = {Acad\'emie des sciences, Paris},
volume = {359},
number = {1},
year = {2021},
doi = {10.5802/crmath.143},
language = {en},
url = {http://www.numdam.org/articles/10.5802/crmath.143/}
}
TY - JOUR AU - Israwi, Samer AU - Kalisch, Henrik TI - A Mathematical Justification of the Momentum Density Function Associated to the KdV Equation JO - Comptes Rendus. Mathématique PY - 2021 SP - 39 EP - 45 VL - 359 IS - 1 PB - Académie des sciences, Paris UR - http://www.numdam.org/articles/10.5802/crmath.143/ DO - 10.5802/crmath.143 LA - en ID - CRMATH_2021__359_1_39_0 ER -
%0 Journal Article %A Israwi, Samer %A Kalisch, Henrik %T A Mathematical Justification of the Momentum Density Function Associated to the KdV Equation %J Comptes Rendus. Mathématique %D 2021 %P 39-45 %V 359 %N 1 %I Académie des sciences, Paris %U http://www.numdam.org/articles/10.5802/crmath.143/ %R 10.5802/crmath.143 %G en %F CRMATH_2021__359_1_39_0
Israwi, Samer; Kalisch, Henrik. A Mathematical Justification of the Momentum Density Function Associated to the KdV Equation. Comptes Rendus. Mathématique, Tome 359 (2021) no. 1, pp. 39-45. doi : 10.5802/crmath.143. http://www.numdam.org/articles/10.5802/crmath.143/
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