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Comptes Rendus. Mathématique
Partial differential equations
A Mathematical Justification of the Momentum Density Function Associated to the KdV Equation
Comptes Rendus. Mathématique, Volume 359 (2021) no. 1, pp. 39-45.

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.

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.

Received:
Revised:
Accepted:
Published online:
DOI: https://doi.org/10.5802/crmath.143
Samer Israwi 1; Henrik Kalisch 2

1. Lebanese University, Faculty of Sciences 1, Department of Mathematics, Hadath-Beirut, Lebanon
2. Department of Mathematics, University of Bergen, Postbox 7800, 5020 Bergen, Norway
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Samer Israwi; Henrik Kalisch. A Mathematical Justification of the Momentum Density Function Associated to the KdV Equation. Comptes Rendus. Mathématique, Volume 359 (2021) no. 1, pp. 39-45. doi : 10.5802/crmath.143. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.143/

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