The lifespan of small data solutions in two dimensional capillary water waves
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Publication:2402926
DOI10.1007/s00205-017-1126-zzbMath1375.35347arXiv1406.5471OpenAlexW2964105384MaRDI QIDQ2402926
Publication date: 15 September 2017
Published in: Archive for Rational Mechanics and Analysis (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1406.5471
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Cites Work
- Unnamed Item
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- On the existence and conditional energetic stability of solitary gravity-capillary surface waves on deep water
- A new proof of long-range scattering for critical nonlinear Schrödinger equations.
- On the Cauchy problem for gravity water waves
- Nonlinear fractional Schrödinger equations in one dimension
- Two dimensional water waves in holomorphic coordinates
- On the water-wave equations with surface tension
- Capillary-gravity waves for an incompressible ideal fluid
- Almost global wellposedness of the 2-D full water wave problem
- A theory of solitary water-waves in the presence of surface tension
- Gravity waves on the free surface of an incompressible perfect fluid of finite depth
- Well-posedness in Sobolev spaces of the full water wave problem in 2D
- Multilinear estimates and fractional integration
- Existence and conditional energetic stability of three-dimensional fully localised solitary gravity-capillary water waves
- Global solutions for the gravity water waves system in 2d
- Paraproducts with flag singularities. I: A case study
- Fully localised solitary-wave solutions of the three-dimensional gravity -- capillary water-wave problem
- Multi-linear operators given by singular multipliers
- Global solutions and asymptotic behavior for two dimensional gravity water waves
- Global Analysis of a Model for Capillary Water Waves in Two Dimensions
- Strichartz Estimates for the Water-Wave Problem with Surface Tension
- Nonlinear Water Waves with Applications to Wave-Current Interactions and Tsunamis
- Global bounds for the cubic nonlinear Schrödinger equation (NLS) in one space dimension
- Well-posedness of the free-surface incompressible Euler equations with or without surface tension
- Sobolev estimates for two dimensional gravity water waves
- Normal forms and quadratic nonlinear Klein-Gordon equations
- Uniform decay estimates and the lorentz invariance of the classical wave equation
- Asymptotics for large time of solutions to the nonlinear Schrodinger and Hartree equations
- On the Cauchy problem for a capillary drop. Part I: irrotational motion
- Well-posedness in Sobolev spaces of the full water wave problem in 3-D
- Global Regularity for 2d Water Waves with Surface Tension
- Well-posedness of the water-waves equations
- Well‐posedness for the linearized motion of an incompressible liquid with free surface boundary
- Global Existence for Capillary Water Waves
- Long time solutions for a Burgers-Hilbert equation via a modified energy method
- Long-time Sobolev stability for small solutions of quasi-linear Klein-Gordon equations on the circle
- Strichartz estimates for water waves
- Geometry and a priori estimates for free boundary problems of the Euler's equation
- Scattering and small data completeness for the critical nonlinear Schrödinger equation
- The zero surface tension limit two‐dimensional water waves
- Two dimensional water waves in holomorphic coordinates II: global solutions
- Global solutions for the gravity water waves equation in dimension 3