On the geophysical Green-Naghdi system
type: Item
instance of: scholarly article
title: On the geophysical Green-Naghdi system
zbMATH Open document ID: 1487.35316
author: Lili Fan
author: Haochen Li
author: Hongjun Gao
published in: Journal of Nonlinear Science
publication date: 2022-02-03T00:00:00Z
review text: The Green-Naghdi system helps model coastal oceanography because it considers the dispersive effects neglected by the shallow-water equations. The authors derive a modified Green-Naghdi system with the effect of the Coriolis force, which is a model in the equatorial oceanography to describe the propagation of large-amplitude surface waves. First, they use a semigroup approach to establish the local well-posedness of the system. Then, they investigate the effects of the Coriolis force caused by the Earth's rotation and nonlinearities on local well-posedness and traveling wave solutions. Finally, for different Coriolis parameters, they discuss the traveling wave solutions by employing the qualitative method combined with the bifurcation method of the dynamical system.
reviewed by: P. M. da Silva
Mathematics Subject Classification ID: 35Q35
Mathematics Subject Classification ID: 35Q86
Mathematics Subject Classification ID: 76U05
Mathematics Subject Classification ID: 86A05
Mathematics Subject Classification ID: 35B30
Mathematics Subject Classification ID: 35C07
Mathematics Subject Classification ID: 35A01
Mathematics Subject Classification ID: 35A02
Mathematics Subject Classification ID: 76M60
zbMATH DE Number: 7468882
zbMATH Keywords: geophysical Green-Naghdi equations
zbMATH Keywords: local well-posedness
zbMATH Keywords: traveling wave solutions
MaRDI profile type: Publication
full work available at URL: s00332-021-09773-7
OpenAlex ID: W4205636934
cites work: A Nash-Moser theorem for singular evolution equations. Application to the Serre and Green-Naghdi equations
cites work: Large time existence for 3D water waves and asymptotics
cites work: Model equations for long waves in nonlinear dispersive systems
cites work: An integrable shallow water equation with peaked solitons
cites work: On a shallow-water approximation to the Green-Naghdi equations with the Coriolis effect
cites work: The kinematics and stability of solitary and cnoidal wave solutions of the Serre equations
cites work: Nonlinear Water Waves with Applications to Wave-Current Interactions and Tsunamis
cites work: On equatorial wind waves.
cites work: The hydrodynamical relevance of the Camassa-Holm and Degasperis-Procesi equations
cites work: On an integrable two-component Camassa-Holm shallow water system
cites work: Shallow water equations with a complete Coriolis force and topography
cites work: SOME TRAVELING WAVE SOLITONS OF THE GREEN–NAGHDI SYSTEM
cites work: Traveling wave solutions of the Green-Naghdi system
cites work: Travelling wave solutions for some two-component shallow water models
cites work: Well-posedness and blow-up phenomena for the 2-component Camassa-Holm equation
cites work: Unsteady undular bores in fully nonlinear shallow-water theory
cites work: On the rotation-two-component Camassa-Holm system modelling the equatorial water waves
cites work: An integrable equation governing short waves in a long-wave model
cites work: Shallow water equations for equatorial tsunami waves
cites work: On the theory of water waves
cites work: A derivation of equations for wave propagation in water of variable depth
cites work: A nonlocal shallow-water model arising from the full water waves with the Coriolis effect
cites work: Model equations and traveling wave solutions for shallow-water waves with the Coriolis effect
cites work: An exact solution for equatorial geophysical water waves with an underlying current
cites work: On Pollard's wave solution at the Equator
cites work: Variational derivation of a geophysical Camassa-Holm type shallow water equation
cites work: Variational Derivation of the Green–Naghdi Shallow-Water Equations
cites work: Small-amplitude equatorial water waves with constant vorticity: dispersion relations and particle trajectories
cites work: Large time existence for 1D Green-Naghdi equations
cites work: Classification of traveling wave solutions to the Green-Naghdi model
cites work: Q4075341
cites work: Traveling wave solutions of the Camassa-Holm equation
cites work: A shallow‐water approximation to the full water wave problem
cites work: Linear stability of solitary waves of the Green-Naghdi equations
cites work: Hamiltonian Structure and Linear Stability of Solitary Waves of the Green-Naghdi Equations
cites work: ON A CLASS OF SINGULAR NONLINEAR TRAVELING WAVE EQUATIONS (II): AN EXAMPLE OF GCKdV EQUATIONS
cites work: Equatorial wind waves with capillary effects and stagnation points
cites work: Exact geophysical waves in stratified fluids
cites work: An exact solution for geophysical equatorial edge waves over a sloping beach
cites work: Weakly dispersive nonlinear gravity waves
cites work: Q4304308
cites work: Three‐Dimensional Nonlinear Dispersive Waves on Shear Flows
cites work: Bifurcations and Exact Traveling Wave Solutions of the Celebrated Green–Naghdi Equations
cites work: Q4004269
DOI: 10.1007/S00332-021-09773-7
description: scientific article; zbMATH DE number 7468882