Existence and conditional energetic stability of capillary-gravity solitary water waves by minimisation

DOI10.1007/s00205-004-0310-0zbMath1110.76308OpenAlexW2050988715MaRDI QIDQ1884713

Boris Buffoni

Publication date: 5 November 2004

Published in: Archive for Rational Mechanics and Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00205-004-0310-0

Mathematics Subject Classification ID

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) Variational methods applied to problems in fluid mechanics (76M30) Interfacial stability and instability in hydrodynamic stability (76E17)

Related Items

Orbital stability of internal waves ⋮ Transverse dynamics of two-dimensional gravity-capillary periodic water waves ⋮ Existence by minimisation of solitary water waves on an ocean of infinite depth ⋮ A direct construction of a full family of Whitham solitary waves ⋮ Bifurcation structure and stability of steady gravity water waves with constant vorticity ⋮ A Hamiltonian formulation of water waves with constant vorticity ⋮ Traveling water waves — the ebb and flow of two centuries ⋮ Asymptotic linear stability of solitary water waves ⋮ On the existence and conditional energetic stability of solitary gravity-capillary surface waves on deep water ⋮ No Pure Capillary Solitary Waves Exist in 2D Finite Depth ⋮ On the stability of travelling waves with vorticity obtained by minimization ⋮ Solitary wave solutions to a class of Whitham-Boussinesq systems ⋮ Stability of Benney--Luke Line Solitary Waves in 2 Dimensions ⋮ No solitary waves in 2D gravity and capillary waves in deep water ⋮ Surface waves on steady perfect-fluid flows with vorticity ⋮ Fully localised solitary-wave solutions of the three-dimensional gravity -- capillary water-wave problem ⋮ On the existence and conditional energetic stability of solitary water waves with weak surface tension ⋮ A relaxation result for energies defined on pairs set-function and applications ⋮ A free boundary approach to two-dimensional steady capillary gravity water waves ⋮ Solitary wave solutions of a Whitham-Boussinesq system ⋮ The existence and decay of solitary waves for the Fornberg-Whitham equation ⋮ A variational approach to solitary gravity-capillary interfacial waves with infinite depth ⋮ Solitary wave solutions to a class of modified Green-Naghdi systems ⋮ Existence theory of capillary-gravity waves on water of finite depth ⋮ Orbital Stability: Analysis Meets Geometry ⋮ An existence theory for gravity-capillary solitary water waves ⋮ Orbital stability of solitary waves on a ferrofluid jet ⋮ Existence and symmetry of ground states to the Boussinesq \textit{abcd} systems ⋮ Multi-solitons and Related Solutions for the Water-waves System

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• The concentration-compactness principle in the calculus of variations. The locally compact case. I
• Capillary-gravity waves for an incompressible ideal fluid
• The concentration-compactness principle in the calculus of variations. The locally compact case. II
• Orbital stability of standing waves for some nonlinear Schrödinger equations
• A variational approach to surface solitary waves
• Stability theory of solitary waves in the presence of symmetry. I
• A theory of solitary water-waves in the presence of surface tension
• Surface water waves as saddle points of the energy
• The regularity and local bifurcation of steady periodic water waves
• The rigorous approximation of long-wavelength capillary-gravity waves
• Stability of relative equilibria. I: The reduced energy-momentum method
• Conditional energetic stability of gravity solitary waves in the presence of weak surface tension
• Topology and mechanics. I
• Topology and mechanics. II: The planar \(n\)-body problem
• Impulse, Flow Force and Variational Principles
• Lyapunov stability of ground states of nonlinear dispersive evolution equations
• Existence and dynamic stability of solitary wave solutions of equations arising in long wave propagation
• NONUNIQUENESS OF SOLUTIONS OF THE PROBLEM OF SOLITARY WAVES AND BIFURCATION OF CRITICAL POINTS OF SMOOTH FUNCTIONALS
• On the stability theory of solitary waves
• On the Cauchy problem for a capillary drop. Part I: irrotational motion
• Hamiltonian structure, symmetries and conservation laws for water waves
• On the energetic stability of solitary water waves
• Minimization Methods for Quasi-Linear Problems with an Application to Periodic Water Waves