Global Well-posedness for the Focusing Cubic NLS on the Product Space $\mathbb{R} \times \mathbb{T}^3$

DOI10.1137/20M1364953zbMath1464.35334arXiv2009.01116MaRDI QIDQ4985460

Zehua Zhao, Haitian Yue, Xueying Yu

Publication date: 23 April 2021

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

Full work available at URL: https://arxiv.org/abs/2009.01116

zbMATH Keywords

global well-posednessSobolev embeddingprofile decompositionNLSwaveguide manifold

Mathematics Subject Classification ID

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

Related Items (5)

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 ⋮ Long Time Dynamics for Defocusing Cubic Nonlinear Schrödinger Equations on Three Dimensional Product Space ⋮ On scattering asymptotics for the 2D cubic resonant system

Cites Work

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• The energy-critical defocusing NLS on \({\mathbb{T}}^{3}\)
• Global well-posedness of the energy-critical defocusing NLS on \({\mathbb{R} \times \mathbb{T}^3}\)
• Global well-posedness and scattering for the defocusing, \(L^2\)-critical, nonlinear Schrödinger equation when \(d=2\)
• Global well-posedness of the energy-critical nonlinear Schrödinger equation with small initial data in \(H^1(\mathbb T^3)\)
• Global well-posedness, scattering and blow-up for the energy-critical focusing non-linear wave equation
• Scale-invariant Strichartz estimates on tori and applications
• Global regularity for the energy-critical NLS on \(\mathbb S^3\)
• On scattering for the defocusing nonlinear Schrödinger equation on waveguide \(\mathbb{R}^m \times \mathbb{T}\) (when \(m = 2, 3)\)
• Global well-posedness, scattering and blow-up for the energy-critical, focusing, nonlinear Schrö\-dinger equation in the radial case
• Equations différentielles non linéaires et problème de Yamabe concernant la courbure scalaire
• Best constant in Sobolev inequality
• Fourier transform restriction phenomena for certain lattice subsets and applications to nonlinear evolution equations. I: Schrödinger equations
• Exponential sums and nonlinear Schrödinger equations
• Sobolev spaces on Riemannian manifolds
• The best constant problem in the Sobolev embedding theorem for complete Riemannian manifolds
• On the global well-posedness of energy-critical Schrödinger equations in curved spaces
• On scattering for the cubic defocusing nonlinear Schrödinger equation on the waveguide \(\mathbb{R}^2 \times \mathbb{T}\)
• Well-posedness for energy-critical nonlinear Schrödinger equation on waveguide manifold
• The proof of the \(l^2\) decoupling conjecture
• Global well-posedness and scattering for the energy-critical Schrödinger equation in \(\mathbb R^{3}\)
• Strichartz estimates for partially periodic solutions to Schrödinger equations in \(4d\) and applications
• Global well-posedness for the energy-critical focusing nonlinear Schrödinger equation on \(\mathbb{T}^4\)
• On Scattering for the Quintic Defocusing Nonlinear Schrödinger Equation on R × T²
• Global well-posedness and scattering for the defocusing, $L^{2}$-critical nonlinear Schrödinger equation when $d ≥3$
• The cauchy problem for the critical nonlinear Schrödinger equation in Hs
• Global well-posedness and scattering for the defocusing energy-critical nonlinear Schrödinger equation in R 1+4
• The focusing energy-critical nonlinear Schrödinger equation in dimensions five and higher
• Defocusing Nonlinear Schrödinger Equations
• Global well-posedness and scattering for the focusing, cubic Schrödinger equation in dimension d=4
• On Scattering for the Defocusing Quintic Nonlinear Schrödinger Equation on the Two-Dimensional Cylinder
• Global well-posedness and scattering for the defocusing cubic Schrödinger equation on waveguide ℝ2 × 𝕋2

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