[BD entropie et entropie de Bernis–Friedman]
Dans cette note, on propose un lien général entre la BD entropie introduite par D. Bresch et B. Desjardins pour les équations de Saint-Venant visqueuses et l'entropie dissipative de Bernis–Friedman (notée BF) introduite pour étudier les équations de lubrification. Différentes entropies dissipatives sont obtenues suivant le choix des termes de traînée sur Saint-Venant visqueux. Ce lien entre ces deux outils mathématiques aide, par exemple, à prouver l'existence de solutions faibles positives pour les équations de lubrification en partant de l'existence de solutions faibles positives pour des équations de Saint-Venant visqueuses bien choisies.
In this note, we propose in the full generality a link between the BD entropy introduced by D. Bresch and B. Desjardins for the viscous shallow-water equations and the Bernis–Friedman (called BF) dissipative entropy introduced to study the lubrication equations. Different dissipative entropies are obtained playing with the drag terms on the viscous shallow-water equations. It helps for instance to prove the global existence of nonnegative weak solutions to the lubrication equations starting from the global existence of nonnegative weak solutions to appropriate viscous shallow-water equations.
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@article{CRMATH_2019__357_1_1_0,
author = {Bresch, Didier and Colin, Mathieu and Msheik, Khawla and Noble, Pascal and Song, Xi},
title = {BD entropy and {Bernis{\textendash}Friedman} entropy},
journal = {Comptes Rendus. Math\'ematique},
pages = {1--6},
publisher = {Elsevier},
volume = {357},
number = {1},
year = {2019},
doi = {10.1016/j.crma.2018.11.009},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2018.11.009/}
}
TY - JOUR AU - Bresch, Didier AU - Colin, Mathieu AU - Msheik, Khawla AU - Noble, Pascal AU - Song, Xi TI - BD entropy and Bernis–Friedman entropy JO - Comptes Rendus. Mathématique PY - 2019 SP - 1 EP - 6 VL - 357 IS - 1 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2018.11.009/ DO - 10.1016/j.crma.2018.11.009 LA - en ID - CRMATH_2019__357_1_1_0 ER -
%0 Journal Article %A Bresch, Didier %A Colin, Mathieu %A Msheik, Khawla %A Noble, Pascal %A Song, Xi %T BD entropy and Bernis–Friedman entropy %J Comptes Rendus. Mathématique %D 2019 %P 1-6 %V 357 %N 1 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2018.11.009/ %R 10.1016/j.crma.2018.11.009 %G en %F CRMATH_2019__357_1_1_0
Bresch, Didier; Colin, Mathieu; Msheik, Khawla; Noble, Pascal; Song, Xi. BD entropy and Bernis–Friedman entropy. Comptes Rendus. Mathématique, Tome 357 (2019) no. 1, pp. 1-6. doi : 10.1016/j.crma.2018.11.009. http://www.numdam.org/articles/10.1016/j.crma.2018.11.009/
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