Topography influence on the lake equations in bounded domains

Christophe Lacave, Toan T. Nguyen, Benoit Pausader

Research output: Contribution to journalArticlepeer-review

7 Scopus citations


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 Lp 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 Ḿetivier treating the lake equations with a fixed topography and by Ǵerard-Varet and Lacave treating the Euler equations in singular domains.

Original languageEnglish (US)
Pages (from-to)375-406
Number of pages32
JournalJournal of Mathematical Fluid Mechanics
Issue number2
StatePublished - Jun 2014

All Science Journal Classification (ASJC) codes

  • Mathematical Physics
  • Condensed Matter Physics
  • Computational Mathematics
  • Applied Mathematics


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