On the high–low method for NLS on the hyperbolic space

DOI10.1063/5.0012061zbMath1454.35351arXiv2004.05711OpenAlexW3015734737MaRDI QIDQ5140989

Xueying Yu, Gigliola Staffilani

Publication date: 17 December 2020

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2004.05711

zbMATH Keywords

cubic nonlinear Schrödinger (NLS) initial value problem

Mathematics Subject Classification ID

Scattering theory for PDEs (35P25) A priori estimates in context of PDEs (35B45) NLS equations (nonlinear Schrödinger equations) (35Q55) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Time-dependent Schrödinger equations and Dirac equations (35Q41) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02)

Related Items (3)

Introduction to the Special Issue: In memory of Jean Bourgain ⋮ Global well-posedness for the cubic fractional NLS on the unit disk ⋮ On the high–low method for NLS on the hyperbolic space

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• The energy-critical defocusing NLS on \({\mathbb{T}}^{3}\)
• Global well-posedness and scattering for the defocusing, \(L^2\)-critical, nonlinear Schrödinger equation when \(d=2\)
• Global well-posedness for the mass-critical nonlinear Schrödinger equation on \(\mathbb T\)
• Improved almost Morawetz estimates for the cubic nonlinear Schrödinger equation
• Bootstrapped Morawetz estimates and resonant decomposition for low regularity global solutions of cubic NLS on \(\mathbb R^2\)
• Nonlinear Schrödinger equation on real hyperbolic spaces
• Resolvent estimates on symmetric spaces of noncompact type
• Semilinear Schrödinger flows on hyperbolic spaces: scattering in \(H^{1}\)
• Global existence for 2D nonlinear Schrödinger equations via high --- low frequency decomposition method
• The Cauchy problem for the nonlinear Schrödinger equation in \(H^ 1\)
• Resonant decompositions and the \(I\)-method for the cubic nonlinear Schrödinger equation on \(\mathbb R^2\)
• Scattering theory for radial nonlinear Schrödinger equations on hyperbolic space
• The Cauchy problem for the semilinear quintic Schrödinger equation in one dimension.
• Scattering in the energy space and below for 3D NLS
• Almost conservation laws and global rough solutions to a nonlinear Schrödinger equation.
• Global well-posedness and scattering for the defocusing, cubic nonlinear Schrödinger equation when \(n = 3\) via a linear-nonlinear decomposition
• On the global well-posedness of energy-critical Schrödinger equations in curved spaces
• Global well-posedness and scattering for nonlinear Schrödinger equations with algebraic nonlinearity when \(d = 2,3\) and \(u_0\) is radial
• Global existence, scattering and blow-up for the focusing NLS on the hyperbolic space
• Global well-posedness and scattering for the energy-critical Schrödinger equation in \(\mathbb R^{3}\)
• Global well-posedness and scattering for the defocusing, cubic NLS in \(\mathbb{R}^3\)
• Global well-posedness for a periodic nonlinear Schrödinger equation in 1D and 2D
• Global well-posedness for the \(L^2\) critical nonlinear Schrödinger equation in higher dimensions
• Global well-posedness and scattering for the defocusing, L2-critical, nonlinear Schrödinger equation when d = 1
• Global well-posedness and scattering for the defocusing, $L^{2}$-critical nonlinear Schrödinger equation when $d ≥3$
• Global Well-posedness for the Defocusing, Quintic Nonlinear Schrödinger Equation in One Dimension for Low Regularity Data
• ON THE GLOBAL EXISTENCE OF ROUGH SOLUTIONS OF THE CUBIC DEFOCUSING SCHRÖDINGER EQUATION IN R^{2 + 1}
• The cauchy problem for the critical nonlinear Schrödinger equation in Hs
• Global Well-Posedness and Polynomial Bounds for the DefocusingL²-Critical Nonlinear Schrödinger Equation in ℝ
• Global well-posedness for semi-linear wave equations
• Global existence and scattering for rough solutions of a nonlinear Schrödinger equation on ℝ³
• On the high–low method for NLS on the hyperbolic space
• Global Well-Posedness of the Cubic Nonlinear Schrödinger Equation on Closed Manifolds
• Asymptotic Stability of Harmonic Maps on the Hyperbolic Plane under the Schrödinger Maps Evolution

This page was built for publication: On the high–low method for NLS on the hyperbolic space