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

Abstract : 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.
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Submitted on : Wednesday, October 18, 2017 - 2:25:42 PM
Last modification on : Monday, March 29, 2021 - 11:58:08 AM
Long-term archiving on: : Friday, January 19, 2018 - 1:44:21 PM

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Bernard Di Martino, Boris Haspot, Yohan Penel. Global stability of weak solutions for a multilayer Saint-Venant model with interactions between the layers. Nonlinear Analysis: Hybrid Systems, Elsevier, 2017, 163, pp.177 - 200. ⟨10.1016/j.na.2017.07.010⟩. ⟨hal-01407886v2⟩

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