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Coupling the Navier-Stokes Equations with a Short Term Dynamic of Sand Dunes

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Shape Optimization, Homogenization and Optimal Control

Part of the book series: International Series of Numerical Mathematics ((ISNM,volume 169))

Abstract

Our paper deals about sand transport problem near the seabed. We consider model for short-term dynamics of dune (STDD) and megariple morphodynamics built in (Faye et al., Discrete and Continuous Dynamical Systems, 29; N o3 March 2011, 1001–1030), that we coupled with a Navier-Stokes equations. We study the evolution of the dunes and an existence and uniqueness results are established for coupled short-term model. In this framework we derive an asymptotic expansion with respect to the small parameter 𝜖 of its solution, and characterize the terms of the expansion.

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Acknowledgement

This work is supported by NLAGA project (Non Linear Analysis, Geometry and Applications).

Author information

Authors and Affiliations

  1. Université Alioune Diop de Bambey, UFR SATIC, Laboratoire de Mathématique de la Décision et d’Anlyse Numérique, Equipe de recherche: Analyse Non Linéaire et Géométrie, Bambey, Senegal

    Ibrahima Faye

  2. Université Gaston Berger de Saint Louis, Laboratoire de Mathématique de la Décision et d’Analyse Numérique, St Louis, Senegal

    Mariama Ndiaye

  3. Université Cheikh Anta Diop de Dakar, Laboratoire de Mathématique de la Décision et d’ Analyse Numérique, Dakar-Fann, Senegal

    Diaraf Seck

Authors
  1. Ibrahima Faye
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  2. Mariama Ndiaye
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  3. Diaraf Seck
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Corresponding author

Correspondence to Ibrahima Faye .

Editor information

Editors and Affiliations

  1. FB IV Abt. Mathematik, Universität Trier, Trier, Germany

    Volker Schulz

  2. Département de Mathématiques de la, Université Cheikh Anta Diop de Daka, Dakar-Fann, Senegal

    Diaraf Seck

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Faye, I., Ndiaye, M., Seck, D. (2018). Coupling the Navier-Stokes Equations with a Short Term Dynamic of Sand Dunes. In: Schulz, V., Seck, D. (eds) Shape Optimization, Homogenization and Optimal Control . International Series of Numerical Mathematics, vol 169. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-90469-6_10

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