Global stability of weak solutions for a multilayer Saint-Venant model with interactions between layers

This paper concerns the global stability of weak solutions for the multilayer system introduced by Audusse et al., which models incompressible free surface flows. To do this, it is proven that this model admits the so called BD-entropy and a gain of integrability on the velocity. It allows to obtain enough compactness estimates in order to show the stability of global weak solutions.