Topography influence on the Lake equations in bounded domains

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.

References in corpus (4)

• Global existence and uniqueness for the Lake equations with vanishing topography : elliptic estimates for degenerate equations
• The Two Dimensional Euler Equations on Singular Exterior Domains
• Uniqueness for two dimensional incompressible ideal flow on singular domains
• Weak vorticity formulation for the incompressible Euler equations in domains with boundary

Cited by in corpus (1)

• Vortex motion for the lake equations