On Scattering for the Defocusing Quintic Nonlinear Schrödinger Equation on the Two-Dimensional Cylinder

DOI10.1137/19M1270586zbMath1448.35464arXiv1809.01527OpenAlexW3083883585MaRDI QIDQ5124634

Zehua Zhao, Xing Cheng, Zihua Guo

Publication date: 30 September 2020

Published in: SIAM Journal on Mathematical Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1809.01527

zbMATH Keywords

scatteringwell-posednessnonlinear Schrödinger equationprofile decompositioninteraction Morawetz estimatelong time Strichartz estimatequintic resonant nonlinear Schrödinger system

Mathematics Subject Classification ID

Spectral problems; spectral geometry; scattering theory on manifolds (58J50) Scattering theory for PDEs (35P25) NLS equations (nonlinear Schrödinger equations) (35Q55) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Resonance in context of PDEs (35B34) Scattering theory of linear operators (47A40) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02) PDEs on manifolds (35R01)

Related Items (10)

On the decay property of the cubic fourth-order Schrödinger equation ⋮ On long time behavior of the focusing energy-critical NLS on \(\mathbb{R}^d\times\mathbb{T}\) via semivirial-vanishing geometry ⋮ Global Well-Posedness and Scattering for Fourth-Order Schrödinger Equations on Waveguide Manifolds ⋮ Well-posedness for energy-critical nonlinear Schrödinger equation on waveguide manifold ⋮ On global-in-time Strichartz estimates for the semiperiodic Schrödinger equation ⋮ Global endpoint Strichartz estimates for Schrödinger equations on the cylinder \(\mathbb{R} \times \mathbb{T}\) ⋮ Scattering for the mass super-critical perturbations of the mass critical nonlinear Schrödinger equations ⋮ Global Well-posedness for the Focusing Cubic NLS on the Product Space $\mathbb{R} \times \mathbb{T}^3$ ⋮ Long Time Dynamics for Defocusing Cubic Nonlinear Schrödinger Equations on Three Dimensional Product Space ⋮ On scattering asymptotics for the 2D cubic resonant system

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