Global well-posedness and scattering for the defocusing cubic Schrödinger equation on waveguide ℝ2 × 𝕋2

DOI10.1142/S0219891619500048zbMath1428.35548arXiv1710.09702OpenAlexW2946157470WikidataQ115245206 ScholiaQ115245206MaRDI QIDQ5237472

Zehua Zhao

Publication date: 18 October 2019

Published in: Journal of Hyperbolic Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1710.09702

zbMATH Keywords

well-posednessscattering theoryconcentration compactnessNLSwaveguide manifold

Mathematics Subject Classification ID

Spectral problems; spectral geometry; scattering theory on manifolds (58J50) NLS equations (nonlinear Schrödinger equations) (35Q55) Scattering theory of linear operators (47A40) PDEs on manifolds (35R01)

Related Items (10)

On scattering for the defocusing nonlinear Schrödinger equation on waveguide \(\mathbb{R}^m \times \mathbb{T}\) (when \(m = 2, 3)\) ⋮ 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 ⋮ 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 ⋮ Well-posedness for energy-critical nonlinear Schrödinger equation on waveguide manifold ⋮ On scattering for the cubic defocusing nonlinear Schrödinger equation on the waveguide \(\mathbb{R}^2 \times \mathbb{T}\) ⋮ Global Well-posedness for the Focusing Cubic NLS on the Product Space $\mathbb{R} \times \mathbb{T}^3$ ⋮ On scattering asymptotics for the 2D cubic resonant system

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