On considère un modèle de Saint-Venant avec viscosité et terme de friction en dimension deux, pour lequel on obtient un résultat d'existence globale de solutions faibles. On montre également la convergence de ces solutions vers la solution forte globale des équations quasi-géostrophiques visqueuses avec terme de surface libre pour des données bien préparées.
We consider a two dimensional viscous shallow water model with friction term. The existence of global weak solutions is obtained and convergence to the strong solution of the viscous quasi-geostrophic equation with free surface term is proven in the well prepared case.
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@article{CRMATH_2002__335_12_1079_0,
author = {Bresch, Didier and Desjardins, Beno{\i}̂t},
title = {Sur un mod\`ele de {Saint-Venant} visqueux et sa limite quasi-g\'eostrophique},
journal = {Comptes Rendus. Math\'ematique},
pages = {1079--1084},
publisher = {Elsevier},
volume = {335},
number = {12},
year = {2002},
doi = {10.1016/S1631-073X(02)02610-9},
language = {fr},
url = {http://www.numdam.org/articles/10.1016/S1631-073X(02)02610-9/}
}
TY - JOUR AU - Bresch, Didier AU - Desjardins, Benoı̂t TI - Sur un modèle de Saint-Venant visqueux et sa limite quasi-géostrophique JO - Comptes Rendus. Mathématique PY - 2002 SP - 1079 EP - 1084 VL - 335 IS - 12 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/S1631-073X(02)02610-9/ DO - 10.1016/S1631-073X(02)02610-9 LA - fr ID - CRMATH_2002__335_12_1079_0 ER -
%0 Journal Article %A Bresch, Didier %A Desjardins, Benoı̂t %T Sur un modèle de Saint-Venant visqueux et sa limite quasi-géostrophique %J Comptes Rendus. Mathématique %D 2002 %P 1079-1084 %V 335 %N 12 %I Elsevier %U http://www.numdam.org/articles/10.1016/S1631-073X(02)02610-9/ %R 10.1016/S1631-073X(02)02610-9 %G fr %F CRMATH_2002__335_12_1079_0
Bresch, Didier; Desjardins, Benoı̂t. Sur un modèle de Saint-Venant visqueux et sa limite quasi-géostrophique. Comptes Rendus. Mathématique, Tome 335 (2002) no. 12, pp. 1079-1084. doi : 10.1016/S1631-073X(02)02610-9. http://www.numdam.org/articles/10.1016/S1631-073X(02)02610-9/
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