Water waves over a rough bottom in the shallow water regime

DOI10.1016/j.anihpc.2011.10.004zbMath1329.76069arXiv1110.5155OpenAlexW2123576962MaRDI QIDQ413661

David Lannes, Walter Craig, Catherine Sulem

Publication date: 7 May 2012

Published in: Annales de l'Institut Henri Poincaré. Analyse Non Linéaire (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1110.5155

zbMATH Keywords

shallow waterwater wavesrough bathymetry

Mathematics Subject Classification ID

Water waves, gravity waves; dispersion and scattering, nonlinear interaction (76B15) Stokes and related (Oseen, etc.) flows (76D07) Asymptotic expansions of solutions to PDEs (35C20) Homogenization in context of PDEs; PDEs in media with periodic structure (35B27) Euler equations (35Q31)

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Cites Work

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• Numerical simulation of gravity waves
• Sur les ondes de surface de l'eau avec une justification mathématique des équations des ondes en eau peu profonde
• The modulational regime of three-dimensional water waves and the Davey-Stewartson system
• Large time existence for 3D water waves and asymptotics
• Long wave approximations for water waves
• The long-wave limit for the water wave problem I. The case of zero surface tension
• A Long Wave Approximation for Capillary-Gravity Waves and an Effect of the Bottom
• Influence of bottom topography on long water waves
• Long Nonlinear Waves in Resonance with Topography
• Effective Behavior of Solitary Waves over Random Topography
• Solitary wave dynamics in shallow water over periodic topography
• Apparent diffusion due to topographic microstructure in shallow waters
• Gravity Waves in a Channel with a Rough Bottom
• An existence theory for water waves and the boussinesq and korteweg-devries scaling limits
• Resonant reflection of surface water waves by periodic sandbars
• Homogenization and Two-Scale Convergence
• Nonlinear water waves in channels of arbitrary shape
• Delayed singularity formation in solution of nonlinear wave equations in higher dimensions
• On Hamilton's principle for surface waves
• On generalized Bragg scattering of surface waves by bottom ripples
• Well-posedness of the water-waves equations
• Hamiltonian long–wave expansions for water waves over a rough bottom