Remarks on the equatorial shallow water system

Chloé Mullaert[1]

  • [1] ENS Cachan, Laboratoire Jacques-Louis Lions

Annales de la faculté des sciences de Toulouse Mathématiques (2010)

  • Volume: 19, Issue: 1, page 27-36
  • ISSN: 0240-2963

Abstract

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This article recalls the results given by A. Dutrifoy, A. Majda and S. Schochet in [1] in which they prove an uniform estimate of the system as well as the convergence to a global solution of the long wave equations as the Froud number tends to zero. Then, we will prove the convergence with weaker hypothesis and show that the life span of the solutions tends to infinity as the Froud number tends to zero.

How to cite

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Mullaert, Chloé. "Remarks on the equatorial shallow water system." Annales de la faculté des sciences de Toulouse Mathématiques 19.1 (2010): 27-36. <http://eudml.org/doc/115865>.

@article{Mullaert2010,
abstract = {This article recalls the results given by A. Dutrifoy, A. Majda and S. Schochet in [1] in which they prove an uniform estimate of the system as well as the convergence to a global solution of the long wave equations as the Froud number tends to zero. Then, we will prove the convergence with weaker hypothesis and show that the life span of the solutions tends to infinity as the Froud number tends to zero.},
affiliation = {ENS Cachan, Laboratoire Jacques-Louis Lions},
author = {Mullaert, Chloé},
journal = {Annales de la faculté des sciences de Toulouse Mathématiques},
language = {eng},
month = {1},
number = {1},
pages = {27-36},
publisher = {Université Paul Sabatier, Toulouse},
title = {Remarks on the equatorial shallow water system},
url = {http://eudml.org/doc/115865},
volume = {19},
year = {2010},
}

TY - JOUR
AU - Mullaert, Chloé
TI - Remarks on the equatorial shallow water system
JO - Annales de la faculté des sciences de Toulouse Mathématiques
DA - 2010/1//
PB - Université Paul Sabatier, Toulouse
VL - 19
IS - 1
SP - 27
EP - 36
AB - This article recalls the results given by A. Dutrifoy, A. Majda and S. Schochet in [1] in which they prove an uniform estimate of the system as well as the convergence to a global solution of the long wave equations as the Froud number tends to zero. Then, we will prove the convergence with weaker hypothesis and show that the life span of the solutions tends to infinity as the Froud number tends to zero.
LA - eng
UR - http://eudml.org/doc/115865
ER -

References

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  1. Dutrifoy (A), Majda (A.) and Schochet (S.).— A simple justification of the singular limit for equatorial shallow water dynamics, Communications in Pure and Applied Mathematics, 62, p. 305-443 (2008). Zbl1156.76013
  2. Gallagher (I.) and Saint-Raymond (L.).— Mathematical study of the betaplane model, Mémoires de la Société Mathématique de France (2007). Zbl1151.35070
  3. Gallagher (I.) and Saint-Raymond (L.).— On the influence of the Earth’s rotation on geophysical flows.Mémoires de la Société Mathématique de France (2006). 
  4. Chemin (J.-Y.).— A propos d’un problème de pénalisation de type antisymétrique, Journal de Mathématiques Pures et Appliquées, 76, p. 739-755 (1997). Zbl0896.35103MR1485418
  5. Klainerman (S.) and Majda (A.).— Singular limits of quasilinear hyperbolic systems with large parameters and the incompressible limit of compressible fluids, Communications in Pure and Applied Mathematics, 34, p. 481-524 (1981). Zbl0476.76068MR615627

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