Scattering theory in the energy space for a class of nonlinear Schrödinger equations
From MaRDI portal
Publication:791048
zbMath0535.35069MaRDI QIDQ791048
Publication date: 1985
Published in: Journal de Mathématiques Pures et Appliquées. Neuvième Série (Search for Journal in Brave)
existenceintegral equationCauchy problemscattering theoryenergy spacenonlinear Schrödinger equationswave operatorsnonlinear Klein Gordon equation
Scattering theory for PDEs (35P25) Fixed-point theorems (47H10) Second-order nonlinear hyperbolic equations (35L70) A priori estimates in context of PDEs (35B45) Nonlinear higher-order PDEs (35G20)
Related Items
Unnamed Item, Semilinear Schrödinger flows on hyperbolic spaces: scattering in \(H^{1}\), Averaging of nonlinear Schrödinger equations with time-oscillatory coefficients, The defocusing energy-critical nonlinear Schrödinger equation in higher dimensions, Scattering for the nonlinear Schrödinger equation with a general one-dimensional confinement, Analyticity of the scattering operator for semilinear dispersive equations, Scattering theory for the Schrödinger–Debye system, The dynamics of the 3D NLS with the convolution term, Scattering in the energy space for the NLS with variable coefficients, On the Cauchy problem of 3D energy-critical Schrödinger equations with subcritical perturbations, On the growth of Sobolev norms for the cubic Szegő equation, Quantitative derivation and scattering of the 3D cubic NLS in the energy space, A Fujita-type blowup result and low energy scattering for a nonlinear Schrödinger equation, On nonlinear Schrödinger equations with random initial data, Birkhoff normal form for the nonlinear Schrödinger equation, Asymptotics of wave models for non star-shaped geometries, On the Cauchy problem for the Zakharov system, Large global solutions for nonlinear Schrödinger equations. II: Mass-supercritical, energy-subcritical cases, Pair excitations and the mean field approximation of interacting Bosons. I, Time decay of scaling critical electromagnetic Schrödinger flows, Scattering for stochastic nonlinear Schrödinger equations, Asymptotic dynamics of certain solutions for an extended nonlinear Gross-Pitaevskii equation with critical nonlinear damping in \(\mathbb{R}^3\), Time-dependent method for non-linear Schrödinger equations in inverse scattering problems, Scattering in \(H^{1}\) for the intercritical NLS with an inverse-square potential, My collaboration with Jean Ginibre, Global existence and scattering of equivariant defocusing Chern-Simons-Schrödinger system, Nonlinear coherent states and Ehrenfest time for Schrödinger equation, Defocusing \(\dot{H}^{\frac{ 1}{ 2}} \)-critical inhomogeneous nonlinear Schrödinger equations, The low energy scattering for nonlinear Schrödinger equation, Global dynamics above the ground state energy for the cubic NLS equation in 3D, Global existence and blow-up for the generalized sixth-order Boussinesq equation, The dynamics of the 3D radial NLS with the combined terms, Energy scattering for Schrödinger equation with exponential nonlinearity in two dimensions, On the role of quadratic oscillations in nonlinear Schrödinger equations., Almost sure well-posedness and scattering of the 3D cubic nonlinear Schrödinger equation, \(H^1\) scattering for mass-subcritical NLS with short-range nonlinearity and initial data in \(\Sigma\), A Schrödinger equation with time-oscillating nonlinearity, Scattering theory for nonlinear Schrödinger equations with inverse-square potential, Scattering for solutions of a dissipative nonlinear Schrödinger equation, Energy scattering for nonlinear Klein-Gordon and Schrödinger equations in spatial dimensions 1 and 2, Space-time behavior of propagators for Schrödinger evolution equations with Stark effect, Global strong solutions for nonlinear Schrödinger equations, Strichartz inequalities for Lipschitz metrics on manifolds and nonlinear Schrödinger equation on domains, Scattering for the focusing energy-subcritical nonlinear Schrödinger equation, On asymptotic behavior of solutions to Korteweg-de Vries type equations related to vortex filament with axial flow, Beyond mean field: on the role of pair excitations in the evolution of condensates, Well-posedness for energy-critical nonlinear Schrödinger equation on waveguide manifold, Long range scattering for nonlinear Schrödinger equations in one space dimension, Global well-posedness and scattering for the defocusing mass-critical nonlinear Schrödinger equation for radial data in high dimensions, Global self-similar solutions of a class of nonlinear Schrödinger equations, Large global solutions for nonlinear Schrödinger equations. I: Mass-subcritical cases, Asymptotic behavior for nonlinear Schrödinger equations with critical time-decaying harmonic potential, On the derivative nonlinear Schrödinger equation, Well-Posedness of the Initial Value Problem for the Korteweg-de Vries Equation, Energy scattering theory for electromagnetic NLS in dimension two, Smoothing properties and retarded estimates for some dispersive evolution equations, Global well-posedness of a system from quantum hydrodynamics for small data, Scattering of a 2D Schrödinger equation with exponential growth in the conformal space, Non-radial scattering theory for nonlinear Schrödinger equations with potential, Long range scattering for the Maxwell-Schrödinger system with large magnetic field data and small Schrödinger data, Scattering of solutions to the nonlinear Schrödinger equations with regular potentials, Rapidly decaying solutions of the nonlinear Schrödinger equation, Small solutions to nonlinear Schrödinger equations, Energy scattering for a class of the defocusing inhomogeneous nonlinear Schrödinger equation, Large time behavior of small solutions to subcritical derivative nonlinear Schrödinger equations, Perturbation theory for infinite-dimensional integrable systems on the line. A case study, Global existence and asymptotic behavior of solutions for the Maxwell- Schrödinger equations in three space dimensions, Long range scattering for nonlinear Schrödinger and Hartree equations in space dimension \(n\geq{}2\), On the blow up phenomenon of the critical nonlinear Schrödinger equation, Qualitative aspects for the cubic nonlinear Schrödinger equations with localized damping: exponential and polynomial stabilization, Time local well-posedness for the Benjamin-Ono equation with large initial data, Asyptotic behavior of solutions to nonlinear Schrödinger equations with time-dependent harmonic potentials, The modified energy technique and applications, Rigorous derivation of the Gross-Pitaevskii equation with a large interaction potential, Energy scattering theory for the nonlinear Schrödinger equations with exponential growth in lower spatial dimensions, Scattering and strong instability of the standing waves for dipolar quantum gases, Remarks on global a priori estimates for the nonlinear Schrödinger equation, Some non-existence results for the semilinear Schrödinger equation without gauge invariance, Blow up threshold for the Gross-Pitaevskii system with combined nonlocal nonlinearities, Strichartz estimates and wave equation in a conic singular space, A sharp condition for scattering of the radial 3D cubic nonlinear Schrödinger equation, Sharp asymptotic behavior of solutions for cubic nonlinear Schrödinger equations with a potential, On 2D nonlinear Schrödinger equation on non-trapping exterior domains, Semi-classical Schrödinger equations with harmonic potential and nonlinear perturbation, Nonlinear Schrödinger equations in the Sobolev space of critical order, Tensor products and correlation estimates with applications to nonlinear Schrödinger equations, Scattering in the energy space and below for 3D NLS, \(H^2\)-scattering for systems of weakly coupled Fourth-order NLS equations in low space Dimensions, On blow up for the energy super critical defocusing nonlinear Schrödinger equations, A nonlinear Schrödinger equation with Coulomb potential, Unnamed Item, Scattering theory for the cubic nonlinear Klein-Gordon system, On the ill-posedness of some canonical dispersive equations., Nonrelativistic limit of scattering theory for nonlinear Klein-Gordon equations, \(H^1\)-scattering for systems of \(N\)-defocusing weakly coupled NLS equations in low space dimensions, Sharp \(L^r\) asymptotics of the small solutions to the nonlinear Schrödinger equations, Global wellposedness for 1D nonlinear Schrödinger equation for data with an infinite \(L^2\) norm, Exponential stabilization for the nonlinear Schrödinger equation with localized damping, On the Davey-Stewartson systems, Global well-posedness and instability of an inhomogeneous nonlinear Schrödinger equation, Asymptotic behavior of the solutions of a nonlinear system of schrödinger equations, Quadratic Morawetz inequalities and asymptotic completeness in the energy space for nonlinear Schrödinger and Hartree equations, About the wave equation outside two strictly convex obstacles, On a nonlocal Zakharov equation, On the asymptotic behavior of nonlinear Schrödinger equations with magnetic effect, Blow up threshold for the Gross‐Pitaevskii system with trapped dipolar quantum gases, Focusing intercritical NLS with inverse-square potential, Global existence and scattering for nonlinear Schrödinger equations with time-dependent damping, The initial value problem for the derivative nonlinear Schrödinger equation in the energy space, On the low Mach number limit for 2D Navier-Stokes-Korteweg systems, Global Well-Posedness and Scattering for Mass-Critical, Defocusing, Infinite Dimensional Vector-Valued Resonant Nonlinear Schrödinger System, H m -modified wave operator for nonlinear Hartree equation in space of dimensionn≥2, Well-posedness of the nonlinear Schrödinger equation on the half-plane, Quadratic forms for the 1-D semilinear Schrödinger equation, Global well-posedness of a damped Schrödinger equation in two space dimensions, Self-similar solutions for nonlinear Schrödinger equations, On the Generalized Benjamin-Ono Equation, On 2D nonlinear Schrödinger equations with data on \(\mathbb{R} \times \mathbb{T}\), On the defect of compactness for the Strichartz estimates of the Schrödinger equations, Remarks on the energy scattering for nonlinear Klein-Gordon and Schrödinger equations, Unnamed Item, Finite speed of disturbance for the nonlinear Schrödinger equation, Global wellposedness of defocusing critical nonlinear Schrödinger equation in the radial case, Scattering theory below energy for the cubic fourth-order Schrödinger equation, Dynamics of some coupled nonlinear Schrödinger systems in
