Well-posedness and scattering for nonlinear Schrödinger equations on \(\mathbb{R}^d \times \mathbb{T}\) in the energy space
From MaRDI portal
Publication:515343
DOI10.4171/RMI/911zbMath1365.35164arXiv1409.3938MaRDI QIDQ515343
Nicola Visciglia, Nickolay Tzvetkov
Publication date: 13 March 2017
Published in: Revista Matemática Iberoamericana (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1409.3938
Scattering theory for PDEs (35P25) NLS equations (nonlinear Schrödinger equations) (35Q55) Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs (35B30) Perturbations of PDEs on manifolds; asymptotics (58J37)
Related Items (19)
On scattering for the defocusing nonlinear Schrödinger equation on waveguide \(\mathbb{R}^m \times \mathbb{T}\) (when \(m = 2, 3)\) ⋮ Scattering for the nonlinear Schrödinger equation with a general one-dimensional confinement ⋮ Decay in energy space for the solution of fourth-order Hartree-Fock equations with general non-local interactions ⋮ Small data scattering for energy critical NLKG on product spaces Rd ×ℳ2 ⋮ On long time behavior of the focusing energy-critical NLS on \(\mathbb{R}^d\times\mathbb{T}\) via semivirial-vanishing geometry ⋮ On the Global Well-Posedness for the Periodic Quintic Nonlinear Schrödinger Equation ⋮ Global Well-Posedness and Scattering for Fourth-Order Schrödinger Equations on Waveguide Manifolds ⋮ On Scattering for the Defocusing Quintic Nonlinear Schrödinger Equation on the Two-Dimensional Cylinder ⋮ Large data scattering for NLKG on waveguide ℝd × 𝕋 ⋮ Modified scattering and beating effect for coupled Schrödinger systems on product spaces with small initial data ⋮ On scattering for the cubic defocusing nonlinear Schrödinger equation on the waveguide \(\mathbb{R}^2 \times \mathbb{T}\) ⋮ Well-posedness and scattering for the mass-energy NLS on \(\mathbb{R}^n\times\mathcal{M}^k\) ⋮ Decay and scattering in energy space for the solution of weakly coupled Schrödinger-Choquard and Hartree-Fock equations ⋮ \(H^2\)-scattering for systems of weakly coupled Fourth-order NLS equations in low space Dimensions ⋮ Global well-posedness and scattering for the defocusing cubic Schrödinger equation on waveguide ℝ2 × 𝕋2 ⋮ Remarks on solitary waves and Cauchy problem for Half-wave-Schrödinger equations ⋮ On scattering asymptotics for the 2D cubic resonant system ⋮ \(H^1\)-scattering for systems of \(N\)-defocusing weakly coupled NLS equations in low space dimensions ⋮ Scattering for radial defocusing inhomogeneous bi-harmonic Schrödinger equations
Cites Work
- Unnamed Item
- Rapidly decaying solutions of the nonlinear Schrödinger equation
- Scattering for nonlinear Schrödinger equation under partial harmonic confinement
- Global well-posedness and scattering for the energy-critical Schrödinger equation in \(\mathbb R^{3}\)
- The cauchy problem for the critical nonlinear Schrödinger equation in Hs
- Tensor products and correlation estimates with applications to nonlinear Schrödinger equations
- INHOMOGENEOUS STRICHARTZ ESTIMATES
- Strichartz inequalities and the nonlinear Schrodinger equation on compact manifolds
This page was built for publication: Well-posedness and scattering for nonlinear Schrödinger equations on \(\mathbb{R}^d \times \mathbb{T}\) in the energy space