Geodesic
Lubrication and shallow-water systems Bernis-Friedman and BD entropies
Didier Bresch1 ; Mathieu Colin2 ; Khawla Msheik1 ; Pascal Noble3 ; Xi Song4
1 Laboratoire de Mathématiques UMR5127 CNRS, Université Savoie Mont-Blanc
2 Equipe INRIA CARDAMOM, IMB Equipes EDP, 351 cours de la libération, 33405 Talence, France
3 IMT, INSA Toulouse, 135 avenue de Rangueil, 31077 Toulouse Cedex 9, France
4
ESAIM. Proceedings, Tome 69 (2020), pp. 1-23.

Voir la notice de l'article provenant de 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.
DOI : 10.1051/proc/202069001

Didier Bresch 1 ; Mathieu Colin 2 ; Khawla Msheik 1 ; Pascal Noble 3 ; Xi Song 4

1 Laboratoire de Mathématiques UMR5127 CNRS, Université Savoie Mont-Blanc
2 Equipe INRIA CARDAMOM, IMB Equipes EDP, 351 cours de la libération, 33405 Talence, France
3 IMT, INSA Toulouse, 135 avenue de Rangueil, 31077 Toulouse Cedex 9, France
4 
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     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},
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     doi = {10.1051/proc/202069001},
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     url = {http://geodesic.mathdoc.fr/articles/10.1051/proc/202069001/}
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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. http://geodesic.mathdoc.fr/articles/10.1051/proc/202069001/

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