Topography influence on the lake equations in bounded domains

Christophe Lacave, Toan Nguyen, Benoit Pausader

Research output: Contribution to journalArticle

1 Citation (Scopus)

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 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
Volume16
Issue number2
DOIs
StatePublished - Jan 1 2014

Fingerprint

Topography
lakes
Lakes
Bounded Domain
topography
Incompressible flow
Three-dimensional Flow
Euler equations
Incompressible Flow
Euler Equations
incompressible flow
Rough
Weak Solution
Byproducts
Horizontal
Perturbation
Fluid
Fluids
Influence
Approximation

All Science Journal Classification (ASJC) codes

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

Cite this

Lacave, Christophe ; Nguyen, Toan ; Pausader, Benoit. / Topography influence on the lake equations in bounded domains. In: Journal of Mathematical Fluid Mechanics. 2014 ; Vol. 16, No. 2. pp. 375-406.
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Topography influence on the lake equations in bounded domains. / Lacave, Christophe; Nguyen, Toan; Pausader, Benoit.

In: Journal of Mathematical Fluid Mechanics, Vol. 16, No. 2, 01.01.2014, p. 375-406.

Research output: Contribution to journalArticle

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