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Modeling shallow water waves (Q5112200)

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scientific article; zbMATH DE number 7206034

Language	Label	Description	Also known as
English	Modeling shallow water waves	scientific article; zbMATH DE number 7206034

Statements

scholarly article

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Modeling shallow water waves (English)

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publication date

28 May 2020

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full work available at URL

https://arxiv.org/abs/2001.09655

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zbMATH Keywords

water waves

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shallow water models

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Boussinesq

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Serre-Green-Naghdi

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Isobe-Kakinuma

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multi-layers models

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vorticity

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MaRDI profile type

MaRDI publication profile

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A comment on the computation of non-conservative products

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Existence of solutions for a Boussinesq system on the half line and on a finite interval

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On the Cauchy problem for gravity water waves

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Large time existence for 3D water waves and asymptotics

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A Nash-Moser theorem for singular evolution equations. Application to the Serre and Green-Naghdi equations

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Regularity and uniqueness of solutions to the Boussinesq system of equations

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Initial-boundary-value problems for the Bona-Smith family of Boussinesq systems

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A multilayer Saint-Venant system with mass exchanges for shallow water flows. Derivation and numerical validation

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Dispersion and nonlinearity of multi-layer non-hydrostatic free-surface flow

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A mathematical study of meteo and landslide tsunamis: the Proudman resonance

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Model equations for long waves in nonlinear dispersive systems

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Artificial boundary conditions for the linearized Benjamin-Bona-Mahony equation

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Discrete transparent boundary conditions for the mixed KDV-BBM equation

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A Boussinesq system for two-way propagation of nonlinear dispersive waves

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Boussinesq equations and other systems for small-amplitude long waves in nonlinear dispersive media. I: Derivation and linear theory

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Boussinesq equations and other systems for small-amplitude long waves in nonlinear dispersive media: II. The nonlinear theory

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Long wave approximations for water waves

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Asymptotic models for internal waves

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A model for the two-way propagation of water waves in a channel

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Large-scale vorticity generation due to dissipating waves in the surf zone

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A splitting approach for the fully nonlinear and weakly dispersive Green-Naghdi model

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Recovering water wave elevation from pressure measurements

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A spectral/\(h p\) element depth-integrated model for nonlinear wave-body interaction

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A two-phase shallow debris flow model with energy balance

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Shallow-Water Equations and Related Topics

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Anelastic Limits for Euler-Type Systems

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A reasoned overview on Boussinesq-type models: the interplay between physics, mathematics and numerics

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Long time existence results for bore-type initial data for BBM-Boussinesq systems

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New long time existence results for a class of Boussinesq-type systems

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An integrable shallow water equation with peaked solitons

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Singularity formations for a surface wave model

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Fully nonlinear long-wave models in the presence of vorticity

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Well-Posedness and shallow-water stability for a new Hamiltonian formulation of the water waves equations with vorticity

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Influence of bottom topography on long water waves

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A double-layer Boussinesq-type model for highly nonlinear and dispersive waves

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Numerical simulation of strongly nonlinear and dispersive waves using a Green-Naghdi model

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Shallow water equations: viscous solutions and inviscid limit

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Nonlinear evolution equations for two-dimensional surface waves in a fluid of finite depth

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Compressible Flow and Euler's Equations

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Recovery of steady periodic wave profiles from pressure measurements at the bed

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Wave breaking for nonlinear nonlocal shallow water equations

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The hydrodynamical relevance of the Camassa-Holm and Degasperis-Procesi equations

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Stability of multidimensional undercompressive shock waves

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Well-posedness of the free-surface incompressible Euler equations with or without surface tension

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Well-posedness in smooth function spaces for moving-boundary 1-D compressible euler equations in physical vacuum

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Well-posedness in smooth function spaces for the moving-boundary three-dimensional compressible Euler equations in physical vacuum

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Solitary water wave interactions

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Hamiltonian long‐wave expansions for free surfaces and interfaces

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Numerical simulation of gravity waves

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Nonlinear modulation of gravity waves: a rigorous approach

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A priori estimates for water waves with emerging bottom

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Convergence of the viscosity method for isentropic gas dynamics

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On initial-boundary value problems for a Boussinesq system of BBM-BBM type in a plane domain

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Boussinesq systems of Bona-Smith type on plane domains: theory and numerical analysis

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Asymptotic models for the generation of internal waves by a moving ship, and the dead-water phenomenon

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Rigorous justification of the Favrie–Gavrilyuk approximation to the Serre–Green–Naghdi model

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Well-posedness of the Green–Naghdi and Boussinesq–Peregrine systems

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A discontinuous Galerkin method for a new class of Green-Naghdi equations on simplicial unstructured meshes

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Analysis of \mathbb{C}P^{N-1} sigma models via projective structures

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On Whitham's conjecture of a highest cusped wave for a nonlocal dispersive equation

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A rapid numerical method for solving Serre–Green–Naghdi equations describing long free surface gravity waves

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A hierarchy of dispersive layer-averaged approximations of Euler equations for free surface flows

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A multilayer method for the hydrostatic Navier-Stokes equations: a particular weak solution

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A flexible genuinely nonlinear approach for nonlinear wave propagation, breaking and run-up

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Geometric evolution of the Reynolds stress tensor

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Congested shallow water model: roof modeling in free surface flow

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A derivation of equations for wave propagation in water of variable depth

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Entropy viscosity method for nonlinear conservation laws

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On the pressure transfer function for solitary water waves with vorticity

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Prediction of the free-surface elevation for rotational water waves using the recovery of pressure at the bed

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Global well-posedness of the BCL system with viscosity

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Wave breaking in the Whitham equation

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A shallow water approximation for water waves

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Isobe-Kakinuma model for water waves as a higher order shallow water approximation

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A mathematical justification of the Isobe-Kakinuma model for water waves with and without bottom topography

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Hyperbolic free boundary problems and applications to wave-structure interactions

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Recent advances on the global regularity for irrotational water waves

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Derivation and analysis of a new 2D Green–Naghdi system

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Variable depth KdV equations and generalizations to more nonlinear regimes

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Large time existence for 1D Green-Naghdi equations

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Well-posedness for compressible Euler equations with physical vacuum singularity

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Well-posedness of Compressible Euler Equations in a Physical Vacuum

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A new model of shoaling and breaking waves: one-dimensional solitary wave on a mild sloping beach

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A derivation of the Green-Naghdi equations for irrotational flows

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On Whitham and Related Equations

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Numerical study of blow up and stability of solutions of generalized Kadomtsev-Petviashvili equations

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The scattering problem for Hamiltonian ABCD Boussinesq systems in the energy space

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Well-posedness of the water-waves equations

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On the dynamics of floating structures

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Derivation of asymptotic two-dimensional time-dependent equations for surface water wave propagation

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Nonlinear Wave–Current Interactions in Shallow Water

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The shoreline problem for the one-dimensional shallow water and Green-Naghdi equations

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Weakly transverse Boussinesq systems and the Kadomtsev–Petviashvili approximation

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Remarks on the full dispersion Kadomtsev-Petviashvli equation

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Mathematics and physics

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A shallow‐water approximation to the full water wave problem

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Well-Posedness of Strongly Dispersive Two-Dimensional Surface Wave Boussinesq Systems

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Well-posedness for the motion of an incompressible liquid with free surface boundary

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Compressible flow with vacuum and physical singularity.

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Shock formation in solutions to the \(2D\) compressible Euler equations in the presence of non-zero vorticity

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A variational principle for a fluid with a free surface

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The existence of multidimensional shock fronts

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The stability of multidimensional shock fronts

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Compressible fluid flow and systems of conservation laws in several space variables

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Nonlinear evolutions of surface gravity waves on fluid of finite depth

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Nonlinear evolution of surface gravity waves over an uneven bottom

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Hamiltonian structure for two-dimensional extended Green–Naghdi equations

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Coriolis effect on water waves

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The Cauchy problem on large time for a Boussinesq-Peregrine equation with large topography variations

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On Hamilton's principle for surface waves

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On the Korteweg—de Vries equation for a gradually varying channel

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Long-Time Existence of Solutions to Boussinesq Systems

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Solvability of the initial value problem to a model system for water waves

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Solvability of the initial value problem to the Isobe-Kakinuma model for water waves

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Recovering the Water-Wave Profile from Pressure Measurements

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Long waves on a beach

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Modelling turbulence generation in solitary waves on shear shallow water flows

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A new model of shoaling and breaking waves. Part 2. Run-up and two-dimensional waves

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A new model of roll waves: comparison with Brock’s experiments

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The classical hydraulic jump in a model of shear shallow-water flows

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The Cauchy Problem on Large Time for Surface-Waves-Type Boussinesq Systems II

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The Cauchy problem on large time for surface waves Boussinesq systems

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The long-wave limit for the water wave problem I. The case of zero surface tension

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The compressible Euler equations in a bounded domain: Existence of solutions and the incompressible limit

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Existence of solutions for the Boussinesq system of equations

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A priori estimates for fluid interface problems

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An accurate and efficient finite-difference algorithm for non-hydrostatic free-surface flow with application to wave propagation

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Korteweg-de Vries Equation and Generalizations. III. Derivation of the Korteweg-de Vries Equation and Burgers Equation

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Finite time analyticity for the two and three dimensional Kelvin- Helmholtz instability

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Uni-directional waves over slowly varying bottom. I: Derivation of a KdV- type of equation

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Water-wave profiles from pressure measurements: extensions

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A fully nonlinear Boussinesq model for surface waves. Part 1. Highly nonlinear unsteady waves

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Variational methods and applications to water waves

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Well-posedness in Sobolev spaces of the full water wave problem in 2D

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Well-posedness in Sobolev spaces of the full water wave problem in 3-D

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The initial-boundary value problem for the ``good'' Boussinesq equation on the bounded domain

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Identifiers

zbMATH Open document ID

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10.1088/1361-6544/ab6c7c

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Mathematics Subject Classification ID

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zbMATH DE Number

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Sitelinks

Mathematics(1 entry)

mardi Publication:5112200

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