BD Entropy and Bernis-Friedman Entropy

Abstract : 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 lubrications equations. Di erent dissipative entropies are obtained playing with the drag terms on the viscous shallow water equations. It helps for instance to prove global existence of nonnegative weak solutions for the lubrication equations starting from the global existence of nonnegative weak solutions for appropriate viscous shallow-water equations.
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Contributor : Khawla Msheik <>
Submitted on : Tuesday, November 6, 2018 - 10:25:09 AM
Last modification on : Friday, April 12, 2019 - 4:22:52 PM
Long-term archiving on : Thursday, February 7, 2019 - 12:48:33 PM


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  • HAL Id : hal-01911965, version 1
  • ARXIV : 1811.02794


Didier Bresch, Mathieu Colin, Khawla Msheik, Pascal Noble, Xi Song. BD Entropy and Bernis-Friedman Entropy. 2018. ⟨hal-01911965v1⟩



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