Lubrication and shallow-water systems Bernis-Friedman and BD entropies
ESAIM. Proceedings, Tome 69 (2020), pp. 1-23
Cet article a éte moissonné depuis la source EDP Sciences
This paper concerns the results recently announced by the authors, in C.R. Acad. Sciences Maths volume 357, Issue 1, 1-6 (2019), which make the link between the BD entropy introduced by D. Bresch and B. Desjardins for the viscous shallow-water equations and the Bernis-Friedman (called BF in our paper) dissipative entropy introduced to study the lubrication equations. More precisely different dissipative BF entropies are obtained from the BD entropies playing with drag terms and capillarity formula for viscous shallow water type equations. This is the main idea in the paper which makes the link between two communities. The limit processes employ the standard compactness arguments taking care of the control in the drag terms. It allows in one dimension for instance to prove global existence of nonnegative weak solutions for lubrication equations starting from the global existence of nonnegative weak solutions for appropriate viscous shallow-water equations (for which we refer to appropriate references). It also allows to prove global existence of nonnegative weak solutions for fourth-order equation including the Derrida-Lebowitz-Speer-Spohn equation starting from compressible Navier-Stokes type equations.
Affiliations des auteurs :
Didier Bresch 1 ; Mathieu Colin 2 ; Khawla Msheik 1 ; Pascal Noble 3 ; Xi Song 4
@article{EP_2020_69_a1,
author = {Didier Bresch and Mathieu Colin and Khawla Msheik and Pascal Noble and Xi Song},
title = {Lubrication and shallow-water systems {Bernis-Friedman} and {BD} entropies},
journal = {ESAIM. Proceedings},
pages = {1--23},
year = {2020},
volume = {69},
doi = {10.1051/proc/202069001},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1051/proc/202069001/}
}
TY - JOUR AU - Didier Bresch AU - Mathieu Colin AU - Khawla Msheik AU - Pascal Noble AU - Xi Song TI - Lubrication and shallow-water systems Bernis-Friedman and BD entropies JO - ESAIM. Proceedings PY - 2020 SP - 1 EP - 23 VL - 69 UR - http://geodesic.mathdoc.fr/articles/10.1051/proc/202069001/ DO - 10.1051/proc/202069001 LA - en ID - EP_2020_69_a1 ER -
%0 Journal Article %A Didier Bresch %A Mathieu Colin %A Khawla Msheik %A Pascal Noble %A Xi Song %T Lubrication and shallow-water systems Bernis-Friedman and BD entropies %J ESAIM. Proceedings %D 2020 %P 1-23 %V 69 %U http://geodesic.mathdoc.fr/articles/10.1051/proc/202069001/ %R 10.1051/proc/202069001 %G en %F EP_2020_69_a1
Didier Bresch; Mathieu Colin; Khawla Msheik; Pascal Noble; Xi Song. Lubrication and shallow-water systems Bernis-Friedman and BD entropies. ESAIM. Proceedings, Tome 69 (2020), pp. 1-23. doi: 10.1051/proc/202069001
Cité par Sources :