BD Entropy and Bernis-Friedman Entropy

Didier Bresch (1) , Khawla Msheik (1) , Pascal Noble (2)

1 LAMA - Laboratoire de Mathématiques
2 IMT - Institut de Mathématiques de Toulouse UMR5219

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. (C) 2018 Published by Elsevier Masson SAS on behalf of Academie des sciences.

Domaines: Equations aux dérivées partielles [math.AP]

Didier Bresch, Khawla Msheik, Pascal Noble. BD Entropy and Bernis-Friedman Entropy. CRAS Compte Rendu Académie des Sciences, 2019, 357 (1), pp.1-6. ⟨10.1016/j.crma.2018.11.009⟩. ⟨hal-02364627⟩