Well-posedness of the Green–Naghdi and Boussinesq–Peregrine systems
Annales mathématiques Blaise Pascal, Volume 25 (2018) no. 1, pp. 21-74.

In this paper we address the Cauchy problem for two systems modeling the propagation of long gravity waves in a layer of homogeneous, incompressible and inviscid fluid delimited above by a free surface, and below by a non-necessarily flat rigid bottom. Concerning the Green–Naghdi system, we improve the result of Alvarez–Samaniego and Lannes [5] in the sense that much less regular data are allowed, and no loss of derivatives is involved. Concerning the Boussinesq–Peregrine system, we improve the lower bound on the time of existence provided by Mésognon-Gireau [40]. The main ingredient is a physically motivated change of unknowns revealing the quasilinear structure of the systems, from which energy methods are implemented.

Published online:
DOI: 10.5802/ambp.372
Classification: 35L45,  35Q35,  76B15
Keywords: Well-posedness theory, shallow water models, quasilinear dispersive systems
Vincent Duchêne 1; Samer Israwi 2

1 Univ. Rennes 1, CNRS, IRMAR - UMR 6625, 35000 Rennes, France
2 Mathématiques, Faculté des sciences I et École doctorale des sciences et technologie Université Libanaise Beyrouth, Liban
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
     author = {Vincent Duch\^ene and Samer Israwi},
     title = {Well-posedness of the {Green{\textendash}Naghdi} and {Boussinesq{\textendash}Peregrine} systems},
     journal = {Annales math\'ematiques Blaise Pascal},
     pages = {21--74},
     publisher = {Universit\'e Clermont Auvergne, Laboratoire de math\'ematiques Blaise Pascal},
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Vincent Duchêne; Samer Israwi. Well-posedness of the Green–Naghdi and Boussinesq–Peregrine systems. Annales mathématiques Blaise Pascal, Volume 25 (2018) no. 1, pp. 21-74. doi : 10.5802/ambp.372. https://ambp.centre-mersenne.org/articles/10.5802/ambp.372/

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