Large time existence for 1D Green-Naghdi equations

DOI10.1016/j.na.2010.08.019zbMath1381.86012arXiv0909.2232OpenAlexW2127230707MaRDI QIDQ603019

Samer Israwi

Publication date: 5 November 2010

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0909.2232

zbMATH Keywords

water wavesGreen-Naghdi equationsPicard iterative scheme

Mathematics Subject Classification ID

Hydrology, hydrography, oceanography (86A05) Water waves, gravity waves; dispersion and scattering, nonlinear interaction (76B15) Theoretical approximation in context of PDEs (35A35) PDEs in connection with geophysics (35Q86)

Related Items

Global existence for small data of the viscous Green-Naghdi type equations ⋮ Existence of a regular solution for 1D Green-Naghdi equations with surface tension at a large time instant ⋮ On a shallow-water approximation to the Green-Naghdi equations with the Coriolis effect ⋮ A Class of Boundary Conditions for Time-Discrete Green--Naghdi Equations with Bathymetry ⋮ Medium amplitude model for internal waves over large topography variation ⋮ Mathematical modeling and numerical analysis for the higher order Boussinesq system ⋮ A numerical scheme for an improved Green-Naghdi model in the Camassa-Holm regime for the propagation of internal waves ⋮ Well-posedness of the Green–Naghdi and Boussinesq–Peregrine systems ⋮ The shoreline problem for the one-dimensional shallow water and Green-Naghdi equations ⋮ Numerical study of the Serre-Green-Naghdi equations and a fully dispersive counterpart ⋮ On the blow-up scenario for some modified Serre-Green-Naghdi equations ⋮ Shallow water asymptotic models for the propagation of internal waves ⋮ Derivation and well-posedness of the extended Green-Naghdi equations for flat bottoms with surface tension ⋮ Error Estimates for Galerkin Approximations of the Serre Equations ⋮ A new symmetric interior penalty discontinuous Galerkin formulation for the <scp>Serre–Green–Naghdi</scp> equations ⋮ Classification of traveling wave solutions to the Green-Naghdi model ⋮ Full justification for the extended Green-Naghdi system for an uneven bottom with/without surface tension ⋮ A shallow water modeling with the Coriolis effect coupled with the surface tension ⋮ Recent advances in Serre-Green-Naghdi modelling for wave transformation, breaking and runup processes ⋮ On the local well‐posedness of the 1D Green–Naghdi system on Sobolev spaces ⋮ Modeling shallow water waves ⋮ Improved local existence result of the Green-Naghdi equations with the Coriolis effect ⋮ Weighted interior penalty discretization of fully nonlinear and weakly dispersive free surface shallow water flows ⋮ A numerical study of variable depth KdV equations and generalizations of Camassa-Holm-like equations ⋮ On the Galerkin/finite-element method for the Serre equations ⋮ An explicit solution with correctors for the Green-Naghdi equations ⋮ On the generalized nonlinear Camassa-Holm equation ⋮ Galerkin finite element methods for the numerical solution of two classical-Boussinesq type systems over variable bottom topography ⋮ Mechanical balance laws for fully nonlinear and weakly dispersive water waves ⋮ A new class of fully nonlinear and weakly dispersive Green-Naghdi models for efficient 2D simulations ⋮ On the Green-Naghdi equations with surface tension in the Camassa-Holm scale ⋮ Explicit solutions and numerical simulations for an asymptotic water waves model with surface tension ⋮ Hamiltonian regularisation of the unidimensional barotropic Euler equations ⋮ An explicit solution with correctors for variable depth KdV and Camassa-Holm-like equations ⋮ Large-time existence for one-dimensional Green-Naghdi equations with vorticity ⋮ Existence results for a monophasic compressible Darcy-Brinkman's flow in porous media ⋮ On the geophysical Green-Naghdi system ⋮ Well-posedness and derivative blow-up for a dispersionless regularized shallow water system ⋮ TRAVELING WAVE SOLUTIONS OF THE GREEN–NAGHDI SYSTEM ⋮ Long, intermediate and short-term well-posedness of high precision shallow-water models with topography variations ⋮ Corrigendum: Error Estimates for Galerkin Approximations of the Serre Equations ⋮ DECOUPLED AND UNIDIRECTIONAL ASYMPTOTIC MODELS FOR THE PROPAGATION OF INTERNAL WAVES

Cites Work

• Unnamed Item
• Gravity waves on the free surface of an incompressible perfect fluid of finite depth
• Well-posedness in Sobolev spaces of the full water wave problem in 2D
• Large time existence for 3D water waves and asymptotics
• Variable depth KdV equations and generalizations to more nonlinear regimes
• An existence theory for water waves and the boussinesq and korteweg-devries scaling limits
• On the theory of water waves
• A derivation of equations for wave propagation in water of variable depth
• Well-posedness in Sobolev spaces of the full water wave problem in 3-D
• Well-posedness of the water-waves equations
• A new Boussinesq method for fully nonlinear waves from shallow to deep water
• A fully nonlinear Boussinesq model for surface waves. Part 1. Highly nonlinear unsteady waves
• Derivation of asymptotic two-dimensional time-dependent equations for surface water wave propagation
• A Nash-Moser theorem for singular evolution equations. Application to the Serre and Green-Naghdi equations
• A shallow‐water approximation to the full water wave problem