Formal derivation and existence of global weak solutions of an energetically consistent viscous sedimentation model

Yacouba ZONGO; Brahima Roamba; Boulaye  Yira; W. W. Jean De Dieu  ZABSONRE

doi:10.26637/mjm1203/008

Abstract

The purpose of this paper is to derive a viscous sedimentation model from the Navier-Stokes system for incompressible flows with a free moving boundary. The derivation is based on the different properties of the fluids; thus, we perform a multiscale analysis in space and time, and a different asymptotic analysis to derive a system coupling two different models: the sediment transport equation for the lower layer and the shallow water model for the upper one. We finally prove the existence of global weak solutions in time for model containing some additional terms.

Keywords:

Saint-Venant-Exner, viscosity, bedload, Reynolds equation, sedimentation, , existence theorems, speed of convergence

Mathematics Subject Classification:

35Q30, 76D05, 86A05, 35Q35

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Yacouba ZONGO Département de Mathématiques, Ecole Polytechnique de Ouagadougou, Burkina Faso.
Brahima Roamba Département de Mathématiques, Université Nazi BONI, Burkina Faso.
Boulaye Yira Département de Mathématiques, Université Nazi BONI, Burkina Faso.
W. W. Jean De Dieu ZABSONRE Département de Mathématiques, Université Nazi BONI, Burkina Faso.

Pages: 307-329
Date Published: 01-07-2024
Vol. 12 No. 03 (2024): Malaya Journal of Matematik (MJM)

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