The water wave problem and Hamiltonian transformation theory
From MaRDI portal
Publication:2230447
DOI10.1007/978-3-030-67845-6_4zbMath1479.76013OpenAlexW3158298774MaRDI QIDQ2230447
Walter Craig, Catherine Sulem, Philippe Guyenne
Publication date: 17 September 2021
Full work available at URL: https://doi.org/10.1007/978-3-030-67845-6_4
existenceuniquenesssurface gravity waveDirichlet-Neumann operatorhead-on soliton collisionshallow water long wave
PDEs in connection with fluid mechanics (35Q35) KdV equations (Korteweg-de Vries equations) (35Q53) Water waves, gravity waves; dispersion and scattering, nonlinear interaction (76B15) Asymptotic methods, singular perturbations applied to problems in fluid mechanics (76M45) Hamilton's equations (70H05) Solitary waves for incompressible inviscid fluids (76B25)
Related Items
A Hamiltonian Dysthe equation for deep-water gravity waves with constant vorticity, Hamiltonian Dysthe Equation for Three-Dimensional Deep-Water Gravity Waves
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Justification of the nonlinear Schrödinger equation for the evolution of gravity driven 2D surface water waves in a canal of finite depth
- Strichartz estimates and local existence for the gravity-capillary waves with non-Lipschitz initial velocity
- Mapping properties of normal forms transformations for water waves
- Finite time singularities for the free boundary incompressible Euler equations
- On the finite-time splash and splat singularities for the 3-D free-surface Euler equations
- A rigorous justification of the modulation approximation to the 2D full water wave problem
- Some properties on the surfaces of vector fields and its application to the Stokes and Navier-Stokes problems with mixed boundary conditions
- Global wellposedness of the 3-D full water wave problem
- Basic properties of solution of the non-steady Navier-Stokes equations with mixed boundary conditions in a bounded domain
- Hamiltonian long-wave approximations of water waves with constant vorticity
- A Hamiltonian approach to nonlinear modulation of surface water waves
- Numerical simulation of gravity waves
- On the integrable variant of the Boussinesq system: Painlevé property, rational solutions, a related many-body system, and equivalence with the AKNS hierarchy
- Numerical simulation of three-dimensional nonlinear water waves
- On the Navier-Stokes system with pressure boundary condition
- Note on the modified nonlinear Schrödinger equation for deep water waves
- A mathematical justification for Korteweg-de Vries equation and Boussinesq equation of water surface waves
- Stability theory of solitary waves in the presence of symmetry. I
- Sur les ondes de surface de l'eau avec une justification mathématique des équations des ondes en eau peu profonde
- Gravity waves on the free surface of an incompressible perfect fluid of finite depth
- Local solutions to the Navier-Stokes equations with mixed boundary conditions
- Traveling water waves: Spectral continuation methods with parallel implementation
- The nonlinear Schrödinger equation. Self-focusing and wave collapse
- Well-posedness in Sobolev spaces of the full water wave problem in 2D
- The modulational regime of three-dimensional water waves and the Davey-Stewartson system
- Hamiltonian long-wave approximations to the water-wave problem
- An existence theorem for the Boussinesq equations with non-Dirichlet boundary conditions.
- A high-order spectral method for nonlinear water waves in the presence of a linear shear current
- Global solutions of the gravity-capillary water-wave system in three dimensions
- Statistical theory of gravity and capillary waves on the surface of a finite-depth fluid
- Traveling gravity water waves in two and three dimensions.
- Hamiltonian higher-order nonlinear Schrödinger equations for broader-banded waves on deep water
- Is free-surface hydrodynamics an integrable system?
- Long-time existence for multi-dimensional periodic water waves
- Global solutions for the gravity water waves system in 2d
- Normal form transformations and Dysthe's equation for the nonlinear modulation of deep-water gravity waves
- Mixed initial-boundary value problem for the three-dimensional Navier-Stokes equations in polyhedral domains
- A non-steady system with friction boundary conditions for flow of heat-conducting incompressible viscous fluids
- Internal waves coupled to surface gravity waves in three dimensions
- The Whitham equation as a model for surface water waves
- Traveling quasi-periodic water waves with constant vorticity
- The long-wave limit for the water wave problem I. The case of zero surface tension
- A Higher-Order Water-Wave Equation and the Method for Solving It
- Normal Form Transformations for Capillary-Gravity Water Waves
- Envelope Equations for Three-Dimensional Gravity and Flexural-Gravity Waves Based on a Hamiltonian Approach
- Solutions to the Navier-Stokes equations with mixed boundary conditions in two-dimensional bounded domains
- The surface signature of internal waves
- An Introduction to the Mathematical Theory of the Navier-Stokes Equations
- Nonlinear Water Waves with Applications to Wave-Current Interactions and Tsunamis
- Hamiltonian form of the modified nonlinear Schrödinger equation for gravity waves on arbitrary depth
- Numerical study of three-dimensional overturning waves in shallow water
- Well-posedness of the Cauchy problem for models of large amplitude internal waves
- Well-posedness of the free-surface incompressible Euler equations with or without surface tension
- A Long Wave Approximation for Capillary-Gravity Waves and an Effect of the Bottom
- Long wave expansions for water waves over random topography
- Water waves over a random bottom
- A High-Order Spectral Method for Nonlinear Water Waves over Moving Bottom Topography
- Hamiltonian perturbation theory and water waves
- An existence theory for water waves and the boussinesq and korteweg-devries scaling limits
- The stability of solitary waves
- The equations of motion of a perfect fluid with free boundary are not well posed.
- Note on a modification to the nonlinear Schrödinger equation for application to deep water waves
- Nonlinear modulation of gravity waves: a rigorous approach
- Well-posedness in Sobolev spaces of the full water wave problem in 3-D
- On reduced equations in the Hamiltonian theory of weakly nonlinear surface waves
- Do true elevation gravity–capillary solitary waves exist? A numerical investigation
- Recent advances on the global regularity for irrotational water waves
- Global Regularity for 2d Water Waves with Surface Tension
- Well-posedness of the water-waves equations
- Super compact equation for water waves
- Global Existence for Capillary Water Waves
- Quasi-Periodic Standing Wave Solutions of Gravity-Capillary Water Waves
- Computations of fully nonlinear hydroelastic solitary waves on deep water
- Hamiltonian long–wave expansions for water waves over a rough bottom
- Geometry and a priori estimates for free boundary problems of the Euler's equation
- The numerical computation of freely propagating time-dependent irrotational water waves
- Hamiltonian long‐wave expansions for free surfaces and interfaces
- Two dimensional water waves in holomorphic coordinates II: global solutions
- Solitary water wave interactions
- The instability of liquid surfaces when accelerated in a direction perpendicular to their planes. I
- Global solutions for the gravity water waves equation in dimension 3
- An integrable normal form for water waves in infinite depth
- Boussinesq's equation on the circle
- Multi-symplectic integrators: numerical schemes for Hamiltonian PDEs that conserve symplecticity
