Long, intermediate and short-term well-posedness of high precision shallow-water models with topography variations

DOI10.3934/dcdsb.2022068zbMath1498.35426OpenAlexW4226211095MaRDI QIDQ2083286

Bashar Khorbatly

Publication date: 10 October 2022

Published in: Discrete and Continuous Dynamical Systems. Series B (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/dcdsb.2022068

zbMATH Keywords

well-posednessBoussinesq systemwater wavesbottom topographyhigher-order modelsGreen-Naghdi system

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) PDEs in connection with fluid mechanics (35Q35) Water waves, gravity waves; dispersion and scattering, nonlinear interaction (76B15) Capillarity (surface tension) for incompressible inviscid fluids (76B45) First-order nonlinear hyperbolic equations (35L60) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Initial value problems for first-order hyperbolic systems (35L45) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02)

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The highly nonlinear shallow water equation: local well-posedness, wave breaking data and non-existence of \(sech^2\) solutions ⋮ Improved local existence result of the Green-Naghdi equations with the Coriolis effect

Cites Work

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• Large time existence for 1D Green-Naghdi equations
• Sharp estimates for pseudo-differential operators with symbols of limited smoothness and commutators
• Isobe-Kakinuma model for water waves as a higher order shallow water approximation
• A mathematical justification of the Isobe-Kakinuma model for water waves with and without bottom topography
• Boussinesq equations and other systems for small-amplitude long waves in nonlinear dispersive media. I: Derivation and linear theory
• Partial differential equations. 2: Qualitative studies of linear equations
• Hamiltonian formulation of the extended Green-Naghdi equations
• Long wave approximations for water waves
• Derivation and analysis of a new 2D Green–Naghdi system
• Commutator estimates and the euler and navier-stokes equations
• On the theory of water waves
• A derivation of equations for wave propagation in water of variable depth
• Well-posedness of the Green–Naghdi and Boussinesq–Peregrine systems
• Derivation and well-posedness of the extended Green-Naghdi equations for flat bottoms with surface tension
• Boussinesq equations and other systems for small-amplitude long waves in nonlinear dispersive media: II. The nonlinear theory
• A remark on the well‐posedness of the classical Green–Naghdi system
• Mathematical modeling and numerical analysis for the higher order Boussinesq system
• Modeling shallow water waves
• Long Time Existence for a Strongly Dispersive Boussinesq System
• The Cauchy Problem on Large Time for Surface-Waves-Type Boussinesq Systems II
• Derivation of asymptotic two-dimensional time-dependent equations for surface water wave propagation
• Hamiltonian structure for two-dimensional extended Green–Naghdi equations
• A Nash-Moser theorem for singular evolution equations. Application to the Serre and Green-Naghdi equations

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