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

Bernard Di Martino (1, 2) , Boris Haspot (2, 3) , Yohan Penel (4, 2)

1 SPE - Sciences pour l'environnement
2 ANGE - Numerical Analysis, Geophysics and Ecology
3 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision
4 Cerema Direction Centre-Est - Centre d'Etudes et d'Expertise sur les Risques, l'Environnement, la Mobilité et l'Aménagement - Direction Centre-Est

In this paper we investigate the existence of global weak solutions for the multilayer model introduced by Audusse et al. which is related to incompressible free surface flows. We prove the global stability of weak solutions over the torus. We observe that this model admits the so called BD-entropy and a gain of integrability on the velocity in the spirit of the work of Mellet and Vasseur. It allows us to obtain enough compactness estimates in order to show the stability of global weak solutions.

Mots clés: Saint-Venant multilayer model; free surface flow; degenerate viscosities global weak solutions; Navier-Stokes equations

Domaines: Modélisation et simulation; Equations aux dérivées partielles [math.AP]

Bernard Di Martino, Boris Haspot, Yohan Penel. Global stability of weak solutions for a multilayer Saint-Venant model with interactions between the layers. 2016. ⟨hal-01407886v1⟩