Mullaert, Chloé Remarks on the equatorial shallow water system. (English) Zbl 1187.35181 Ann. Fac. Sci. Toulouse, Math. (6) 19, No. 1, 27-36 (2010). Summary: This article recalls the results given by A. Dutrifoy, A. Majda and S. Schochet in [Commun. Pure Appl. Math. 62, No. 3, 322–333 (2009; Zbl 1156.76013)] 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. We 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. Cited in 1 Document MSC: 35Q35 PDEs in connection with fluid mechanics 76B15 Water waves, gravity waves; dispersion and scattering, nonlinear interaction 86A05 Hydrology, hydrography, oceanography 35B35 Stability in context of PDEs 35B06 Symmetries, invariants, etc. in context of PDEs Citations:Zbl 1156.76013 PDFBibTeX XMLCite \textit{C. Mullaert}, Ann. Fac. Sci. Toulouse, Math. (6) 19, No. 1, 27--36 (2010; Zbl 1187.35181) Full Text: DOI Numdam Numdam EuDML References: [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). · Zbl 1156.76013 [2] Gallagher (I.) and Saint-Raymond (L.).— Mathematical study of the betaplane model, Mémoires de la Société Mathématique de France (2007). · Zbl 1151.35070 [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). · Zbl 0896.35103 [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). · Zbl 0476.76068 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.