Scattering and blow-up for the focusing nonlinear Klein-Gordon equation with complex-valued data
From MaRDI portal
Publication:512465
DOI10.1007/s00023-016-0510-9zbMath1362.35059OpenAlexW2471671661MaRDI QIDQ512465
Publication date: 24 February 2017
Published in: Annales Henri Poincaré (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s00023-016-0510-9
Scattering theory for PDEs (35P25) Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Second-order nonlinear hyperbolic equations (35L70) NLS equations (nonlinear Schrödinger equations) (35Q55) Blow-up in context of PDEs (35B44)
Related Items
Instability of the standing waves for the nonlinear Klein-Gordon equations in one dimension ⋮ Scattering for the mass-critical nonlinear Klein-Gordon equations in three and higher dimensions ⋮ Scattering below the ground state for the 2D non-linear Schrödinger and Klein–Gordon equations revisited
Cites Work
- Blowup and scattering problems for the nonlinear Schrödinger equations
- Global dynamics below the ground state energy for the Zakharov system in the 3D radial case
- On space-time means and everywhere defined scattering operators for nonlinear Klein-Gordon equations
- Invariant manifolds and dispersive Hamiltonian evolution equations
- Scattering for the focusing energy-subcritical nonlinear Schrödinger equation
- Concentration compactness for critical wave maps
- Global well-posedness, scattering and blow-up for the energy-critical focusing non-linear wave equation
- Nonlinear scalar field equations. I: Existence of a ground state
- Global well-posedness, scattering and blow-up for the energy-critical, focusing, nonlinear Schrö\-dinger equation in the radial case
- Scattering for the nonradial 3D cubic nonlinear Schrödinger equation
- On scattering and everywhere defined scattering operators for nonlinear Klein-Gordon equations
- Uniform estimates for solutions of nonlinear Klein-Gordon equations
- Uniqueness of positive solutions of \(\Delta u-u+u^ p=0\) in \(R^ n\)
- Nonlinear scattering theory at low energy
- Blow-up of \(H^ 1\) solution for the nonlinear Schrödinger equation
- Saddle points and instability of nonlinear hyperbolic equations
- Existence of solitary waves in higher dimensions
- Scattering for wave maps exterior to a ball
- Existence of a ground state and scattering for a nonlinear Schrödinger equation with critical growth
- Scattering threshold for the focusing nonlinear Klein-Gordon equation
- Energy scattering for nonlinear Klein-Gordon and Schrödinger equations in spatial dimensions 1 and 2
- A sharp condition for scattering of the radial 3D cubic nonlinear Schrödinger equation
- Scattering below critical energy for the radial 4D Yang-Mills equation and for the 2D corotational wave map system
- Scattering for the cubic Klein–Gordon equation in two space dimensions
- Multi-Solitary Waves for the Nonlinear Klein-Gordon Equation
- Divergence of Infinite-Variance Nonradial Solutions to the 3D NLS Equation
- Blow-Up of H 1 Solutions for the One-Dimensional Nonlinear Schrodinger Equations with Critical Power Nonlinearity
- High Frequency Approximation of Solutions to Critical Nonlinear Wave Equations
- Strong Instability of Standing Waves for the Nonlinear Klein–Gordon Equation and the Klein–Gordon–Zakharov System
- Remarks on the energy scattering for nonlinear Klein-Gordon and Schrödinger equations
