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arXiv · 1811.02794

BD Entropy and Bernis-Friedman Entropy

Didier Bresch·Mathieu Colin·Khawla Msheik·Pascal Noble·Xi Song
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Abstract

In this note, we propose in the full generality a link between the BD entropy introduced by D. Bresch andB. Desjardins for the viscous shallow-water equations and the Bernis-Friedman (called BF) dissipative entropyintroduced to study the lubrications equations. Dierent dissipative entropies are obtained playing with the dragterms on the viscous shallow water equations. It helps for instance to prove global existence of nonnegativeweak solutions for the lubrication equations starting from the global existence of nonnegative weak solutions forappropriate viscous shallow-water equations.

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Didier Bresch, Mathieu Colin, Khawla Msheik, Pascal Noble, Xi Song. 2018-11-07. BD Entropy and Bernis-Friedman Entropy. https://arxiv.org/abs/1811.02794

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