Global weak solutions of the Serre-Green-Naghdi equations with surface tension
DOI10.4171/aihpc/99zbMATH Open1541.35378MaRDI QIDQ6540312
Publication date: 15 May 2024
Published in: Annales de l'Institut Henri Poincaré. Analyse Non Linéaire (Search for Journal in Brave)
Smoothness and regularity of solutions to PDEs (35B65) 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) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Initial value problems for nonlinear higher-order PDEs (35G25) Weak solutions to PDEs (35D30)
Cites Work
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- Global existence for small data of the viscous Green-Naghdi type equations
- On the water-wave equations with surface tension
- Large time existence for 1D Green-Naghdi equations
- Regularity and uniqueness of solutions to the Boussinesq system of equations
- Capillary-gravity waves for an incompressible ideal fluid
- Ordinary differential equations, transport theory and Sobolev spaces
- Well-posedness of the water-wave problem with surface tension
- Compact sets in the space \(L^ p(0,T;B)\)
- Existence of solutions for the Boussinesq system of equations
- On the change of form of long waves advancing in a rectangular canal, and on a new type of long stationary waves.
- Weak solutions to a nonlinear variational wave equation
- Weakly singular shock profiles for a non-dispersive regularization of shallow-water equations
- On weakly singular and fully nonlinear travelling shallow capillary-gravity waves in the critical regime
- Weak solutions to a nonlinear variational wave equation with general data
- The initial value problem for a generalized Boussinesq equation.
- Boussinesq equations and other systems for small-amplitude long waves in nonlinear dispersive media. I: Derivation and linear theory
- Conservative modified Serre-Green-Naghdi equations with improved dispersion characteristics
- On the Green-Naghdi equations with surface tension in the Camassa-Holm scale
- Hamiltonian regularisation of the unidimensional barotropic Euler equations
- Existence of a regular solution for 1D Green-Naghdi equations with surface tension at a large time instant
- Singularity formation for the Serre-Green-Naghdi equations and applications to \textit{abcd}-Boussinesq systems
- On the blow-up scenario for some modified Serre-Green-Naghdi equations
- Non-dispersive conservative regularisation of nonlinear shallow water (and isentropic Euler equations)
- On the fully-nonlinear shallow-water generalized Serre equations
- On the three-dimensional Euler equations with a free boundary subject to surface tension
- Local well-posedness of a Hamiltonian regularisation of the Saint-Venant system with uneven bottom
- On the weak solutions to a shallow water equation.
- RAREFACTIVE SOLUTIONS TO A NONLINEAR VARIATIONAL WAVE EQUATION OF LIQUID CRYSTALS
- A plethora of generalised solitary gravity-capillary water waves
- Surface waves
- The zero surface tension limit of three-dimensional water waves
- Commutator estimates and the euler and navier-stokes equations
- Microlocal defect measures
- On the theory of water waves
- A derivation of equations for wave propagation in water of variable depth
- Thin Films with High Surface Tension
- On the Cauchy problem for a capillary drop. Part I: irrotational motion
- A Modern Introduction to the Mathematical Theory of Water Waves
- An integrable shallow water equation with peaked solitons
- The shoreline problem for the one-dimensional shallow water and Green-Naghdi equations
- Derivation and well-posedness of the extended Green-Naghdi equations for flat bottoms with surface tension
- Korteweg-de Vries Equation and Generalizations. III. Derivation of the Korteweg-de Vries Equation and Burgers Equation
- Focusing at a Point and Absorption of Nonlinear Oscillations
- Bifurcations of Traveling Wave Solutions for Fully Nonlinear Water Waves with Surface Tension in the Generalized Serre–Green–Naghdi Equations
- Well-posedness and derivative blow-up for a dispersionless regularized shallow water system
- Algebraic method for constructing singular steady solitary waves: a case study
- Geometry and a priori estimates for free boundary problems of the Euler's equation
- A Nash-Moser theorem for singular evolution equations. Application to the Serre and Green-Naghdi equations
- Global Weak Solutions to a Generalized Hyperelastic-rod Wave Equation
- A shallow‐water approximation to the full water wave problem
- The zero surface tension limit two‐dimensional water waves
- Essai sur la théorie des eaux courantes.
- Full justification for the extended Green-Naghdi system for an uneven bottom with/without surface tension
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