Formal derivation and existence of global weak solutions of a two-dimensional bilayer model coupling shallow water and Reynolds lubrication equations

2016 ◽  
Vol 99 (3-4) ◽  
pp. 207-239
Author(s):  
Brahima Roamba ◽  
Jean de Dieu Zabsonré ◽  
Sado Traoré
Keyword(s):  
Shallow Water ◽  
Weak Solutions ◽  
Model Coupling ◽  
Two Dimensional ◽  
Global Weak Solutions ◽  
Formal Derivation

scholarly journals AN ENERGETICALLY CONSISTENT VISCOUS SEDIMENTATION MODEL

2009 ◽  
Vol 19 (03) ◽  
pp. 477-499 ◽  
Author(s):  
JEAN DE DIEU ZABSONRÉ ◽  
CARINE LUCAS ◽  
ENRIQUE FERNÁNDEZ-NIETO
Keyword(s):  
Shallow Water ◽  
Weak Solutions ◽  
Numerical Experiments ◽  
Water System ◽  
Two Dimensional ◽  
Sedimentation Model ◽  
Shallow Water System ◽  
Periodic Domains ◽  
The Stability

In this paper we consider a two-dimensional viscous sedimentation model which is a viscous Shallow–Water system coupled with a diffusive equation that describes the evolution of the bottom. For this model, we prove the stability of weak solutions for periodic domains and give some numerical experiments. We also discuss around various discharge quantity choices.

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