Journal of Mathematical Fluid Mechanics

, Volume 16, Issue 2, pp 375–406 | Cite as

Topography Influence on the Lake Equations in Bounded Domains

  • Christophe Lacave
  • Toan T. Nguyen
  • Benoit Pausader
Article

Abstract

We investigate the influence of the topography on the lake equations which describe the two-dimensional horizontal velocity of a three-dimensional incompressible flow. We show that the lake equations are structurally stable under Hausdorff approximations of the fluid domain and L p perturbations of the depth. As a byproduct, we obtain the existence of a weak solution to the lake equations in the case of singular domains and rough bottoms. Our result thus extends earlier works by Bresch and Métivier treating the lake equations with a fixed topography and by Gérard-Varet and Lacave treating the Euler equations in singular domains.

Mathematics Subject Classification (2010)

Primary 35Q35 Secondary 76D03 

Keywords

Existence and uniqueness global weak solutions Hausdorff approximations singular domains rough bottoms 

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Copyright information

© Springer Basel 2013

Authors and Affiliations

  • Christophe Lacave
    • 1
  • Toan T. Nguyen
    • 2
  • Benoit Pausader
    • 3
  1. 1.UMR 7586-CNRS, Institut de Mathématiques de Jussieu-Paris Rive GaucheUniversité Paris-Diderot (Paris 7)Paris Cedex 13France
  2. 2.Department of MathematicsPennsylvania State UniversityUniversity Park, State CollegeUSA
  3. 3.Laboratoire Analyse, Géométrie et ApplicationsUMR 7539, Institut GaliléeUniversité Paris 13France

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