ALVAREZ-SAMANIEGO, Borys; LANNES, David

Métadonnées

Afficher la notice complète

Licence d’utilisation du document

ALVAREZ-SAMANIEGO, Borys
Institut de Mathématiques de Bordeaux [IMB]

LANNES, David
Institut de Mathématiques de Bordeaux [IMB]

Langue

Document de travail - Pré-publication

Résumé en anglais

We rigorously justify in $3D$ the main asymptotic models used in coastal oceanography, including: shallow-water equations, Boussinesq systems, Kadomtsev-Petviashvili (KP) approximation, Green-Naghdi equations, Serre approximation and full-dispersion model. We first introduce a ``variable'' nondimensionalized version of the water-waves equations which vary from shallow to deep water, and which involves four dimensionless parameters. Using a nonlocal energy adapted to the equations, we can prove a well-posedness theorem, uniformly with respect to all the parameters. Its validity ranges therefore from shallow to deep-water, from small to large surface and bottom variations, and from fully to weakly transverse waves. The physical regimes corresponding to the aforementioned models can therefore be studied as particular cases; it turns out that the existence time and the energy bounds given by the theorem are always those needed to justify the asymptotic models. We can therefore derive and justify them in a systematic way.< Réduire

Mots clés en anglais

water-waves

Boussinesq

Shallow-water

Green-Naghdi equations

Serre equations

Dirichlet-Neumann operator

Métadonnées

Partager cette publication !

Licence d’utilisation du document

Large time existence for $3D$ water-waves and asymptotics

Langue

Résumé en anglais

Mots clés en anglais

URI

Origine

Unités de recherche