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.
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Lacave, C., Nguyen, T.T. & Pausader, B. Topography Influence on the Lake Equations in Bounded Domains. J. Math. Fluid Mech. 16, 375–406 (2014). https://doi.org/10.1007/s00021-013-0158-x
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DOI: https://doi.org/10.1007/s00021-013-0158-x