BD Entropy and Bernis-Friedman Entropy
Analysis of PDEs
2018-11-09 v2 Mathematical Physics
Dynamical Systems
math.MP
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.
Cite
@article{arxiv.1811.02794,
title = {BD Entropy and Bernis-Friedman Entropy},
author = {Didier Bresch and Mathieu Colin and Khawla Msheik and Pascal Noble and Xi Song},
journal= {arXiv preprint arXiv:1811.02794},
year = {2018}
}