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.
Mots clés : Well-posedness theory, shallow water models, quasilinear dispersive systems
@article{AMBP_2018__25_1_21_0,
author = {Duch\^ene, Vincent and Israwi, Samer},
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},
volume = {25},
number = {1},
year = {2018},
doi = {10.5802/ambp.372},
language = {en},
url = {http://www.numdam.org/articles/10.5802/ambp.372/}
}
TY - JOUR AU - Duchêne, Vincent AU - Israwi, Samer TI - Well-posedness of the Green–Naghdi and Boussinesq–Peregrine systems JO - Annales mathématiques Blaise Pascal PY - 2018 SP - 21 EP - 74 VL - 25 IS - 1 PB - Université Clermont Auvergne, Laboratoire de mathématiques Blaise Pascal UR - http://www.numdam.org/articles/10.5802/ambp.372/ DO - 10.5802/ambp.372 LA - en ID - AMBP_2018__25_1_21_0 ER -
%0 Journal Article %A Duchêne, Vincent %A Israwi, Samer %T Well-posedness of the Green–Naghdi and Boussinesq–Peregrine systems %J Annales mathématiques Blaise Pascal %D 2018 %P 21-74 %V 25 %N 1 %I Université Clermont Auvergne, Laboratoire de mathématiques Blaise Pascal %U http://www.numdam.org/articles/10.5802/ambp.372/ %R 10.5802/ambp.372 %G en %F AMBP_2018__25_1_21_0
Duchêne, Vincent; Israwi, Samer. Well-posedness of the Green–Naghdi and Boussinesq–Peregrine systems. Annales mathématiques Blaise Pascal, Tome 25 (2018) no. 1, pp. 21-74. doi : 10.5802/ambp.372. http://www.numdam.org/articles/10.5802/ambp.372/
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