Topography Influence on the Lake Equations in Bounded Domains
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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
KeywordsExistence and uniqueness global weak solutions Hausdorff approximations singular domains rough bottoms
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