Derivation and analysis of a new 2D Green-Naghdi system
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | ISRAWI, Samer | |
| dc.date.accessioned | 2024-04-04T02:30:02Z | |
| dc.date.available | 2024-04-04T02:30:02Z | |
| dc.date.created | 2009-12-01 | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/190229 | |
| dc.description.abstractEn | We derive here a variant of the $2D$ Green-Naghdi equations that model the propagation of two-directional, nonlinear dispersive waves in shallow water. This new model has the same accuracy as the standard $2D $ Green-Naghdi equations. Its mathematical interest is that it allows a control of the rotational part of the (vertically averaged) horizontal velocity, which is not the case for the usual Green-Naghdi equations. Using this property, we show that the solution of these new equations can be constructed by a standard Picard iterative scheme so that there is no loss of regularity of the solution with respect to the initial condition. Finally, we prove that the new Green-Naghdi equations conserve the almost irrotationality of the vertically averaged horizontal component of the velocity. | |
| dc.language.iso | en | |
| dc.subject.en | Green-Naghdi equations | |
| dc.subject.en | water-waves | |
| dc.title.en | Derivation and analysis of a new 2D Green-Naghdi system | |
| dc.type | Document de travail - Pré-publication | |
| dc.subject.hal | Mathématiques [math]/Equations aux dérivées partielles [math.AP] | |
| dc.identifier.arxiv | 1001.2850 | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| hal.identifier | hal-00447005 | |
| hal.version | 1 | |
| hal.audience | Non spécifiée | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-00447005v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.au=ISRAWI,%20Samer&rft.genre=preprint |
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