The defocusing energy-critical nonlinear Schrödinger equation in higher dimensions

Monica Vişan

Type: Article

Publication Date: 2007-06-01

Citations: 232

DOI: https://doi.org/10.1215/s0012-7094-07-13825-0

Abstract

We obtain global well-posedness, scattering, and global Lt,x2(n+2)/(n−2) space-time bounds for energy-space solutions to the energy-critical nonlinear Schrodinger (NLS) equation in Rt×Rxn, n≥5

Locations

Duke Mathematical Journal - View
arXiv (Cornell University) - View - PDF

Similar Works

Action	Title	Year	Authors
+	The defocusing energy-critical nonlinear Schrödinger equation in higher dimensions	2005	Monica Vişan
+	Global well-posedness and scattering for the defocusing energy-critical nonlinear Schrödinger equation in $\R^{1+4}$	2005	E. Ryckman Monica Vişan
+	Global well-posedness and scattering for the defocusing energy-critical nonlinear Schrödinger equations of fourth order in dimensions <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" overflow="scroll"><mml:mi>d</mml:mi><mml:mo>⩾</mml:mo><mml:mn>9</mml:mn></mml:math>	2011	Changxing Miao Guixiang Xu Lifeng Zhao
+	Global Well-posedness and Scattering for the Defocusing Cubic nonlinear Schrödinger equation in Four Dimensions	2011	Monica Vişan
+ PDF Chat	Global well-posedness and scattering for the defocusing energy-critical nonlinear Schrödinger equation in R 1+4	2007	E. Ryckman Monica Vişan
+ PDF Chat	Scattering theory for the defocusing fourth-order Schrödinger equation	2016	Changxing Miao Jiqiang Zheng
+	Global well-posedness and scattering for the coupled NLS in critical spaces	2024	Mingming Deng Ying Wang
+	Energy-supercritical NLS: critical $\dot H^s$-bounds imply scattering	2008	Rowan Killip Monica Vişan
+	Energy Critical NLS in two space dimensions	2008	Jim Colliander Slim Ibrahim Mohamed Majdoub Nader Masmoudi
+	Global well-posedness and scattering for the higher-dimensional energy-critical nonlinear Schrödinger equation for radial data.	2005	Terence Tao
+ PDF Chat	ENERGY CRITICAL NLS IN TWO SPACE DIMENSIONS	2009	J. Colliander Sabrin R. M. Ibrahim Mohamed Majdoub Nader Masmoudi
+ PDF Chat	Global well-posedness and scattering of the defocusing energy-critical inhomogeneous nonlinear Schrödinger equation with radial data	2024	Dongjin Park
+	Stability of energy-critical nonlinear Schr\"odinger equations in high dimensions	2005	Terence Tao Monica Vişan
+	Energy-Supercritical NLS: Critical<i>[Hdot]</i><sup><i>s</i></sup>-Bounds Imply Scattering	2010	Rowan Killip Monica Vişan
+	Corrigendum to “Global well-posedness and scattering of the defocusing energy-critical inhomogeneous nonlinear Schrödinger equation with radial data” [J. Math. Anal. Appl. 536 (2) (2024) 128202]	2024	Dongjin Park
+ PDF Chat	Large Global Solutions for the Energy-Critical Nonlinear Schrödinger Equation	2023	Ruobing Bai Jia Shen Yifei Wu
+	Almost Morawetz estimates and global well-posedness for the defocusing $L^2$-critical nonlinear Schr{ö}dinger equation in higher dimensions	2009	Benjamin Dodson
+	Global well-posedness and scattering for the defocusing mass-critical nonlinear Schrödinger equation for radial data in high dimensions	2007	Terence Tao Monica Vişan Xiaoyi Zhang
+	Global well-posedness and scattering for the mass-critical nonlinear Schrödinger equation for radial data in high dimensions	2006	Terence Tao Monica Vişan Xiaoyi Zhang
+	Stability of energy-critical nonlinear Schrödinger equations in high dimensions	2005	Terence Tao Monica Vişan

Works That Cite This (231)

Action	Title	Year	Authors
+	An Lp-theory for almost sure local well-posedness of the nonlinear Schrödinger equations	2018	Oana Pocovnicu Yuzhao Wang
+	Global existence for semilinear Schrödinger equations in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" overflow="scroll"><mml:mn>2</mml:mn><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:math>dimensions	2007	Hua Wang Shangbin Cui
+ PDF Chat	Asymptotic behavior of solutions to fractional diffusion–convection equations	2018	Liviu I. Ignat Diana Stan
+	Global Well-Posedness and Scattering for Fourth-Order Schrödinger Equations on Waveguide Manifolds	2024	Xueying Yu Haitian Yue Zehua Zhao
+ PDF Chat	Numerical simulations for the energy-supercritical nonlinear wave equation	2020	Jason Murphy Yanzhi Zhang
+ PDF Chat	Long-range scattering for a critical homogeneous type nonlinear Schrödinger equation with time-decaying harmonic potentials	2023	Masaki Kawamoto Hayato Miyazaki
+	Global well-posedness and scattering for the energy-critical, defocusing Hartree equation for radial data	2007	Changxing Miao Guixiang Xu Lifeng Zhao
+	Scattering for the radial 3D cubic focusing inhomogeneous nonlinear Schrödinger equation	2017	Luiz Gustavo Farah Carlos M. Guzmán
+	Almost sure scattering for the energy-critical nonlinear wave equation	2019	Bjoern Bringmann
+	Stochastic nonlinear Schrödinger equations in the defocusing mass and energy critical cases	2023	Deng Zhang

Works Cited by This (34)

Action	Title	Year	Authors
+	Singular Integrals and Differentiability Properties of Functions.	1971	Elias M. Stein
+ PDF Chat	Global wellposedness of defocusing critical nonlinear Schrödinger equation in the radial case	1999	Jean Bourgain
+	Harmonic Analysis: Real-variable Methods, Orthogonality, and Oscillatory Integrals	2002	Elias M. Stein Timothy S Murphy
+	GLOBAL WELL-POSEDNESS FOR SCHR ¨ ODINGER EQUATIONS WITH DERIVATIVE ∗	2001	J. Colliander M. Keel Gigliola Staffilani Hideo Takaoka Terence Tao
+	Global existence and scattering for rough solutions of a nonlinear Schrödinger equation on ℝ<sup>3</sup>	2004	J. Colliander M. Keel Gigliola Staffilani Hideo Takaoka Terence Tao
+	Besov Spaces and Unconditional Well-Posedness for the Nonlinear Schrödinger Equation in $\dot{\rm H}^s({\mathbb R}^n)$	2003	Giulia Furioli Elide Terraneo
+	Stability of energy-critical nonlinear Schr\"odinger equations in high dimensions	2005	Terence Tao Monica Vişan
+ PDF Chat	A Strichartz Inequality for the Schrödinger Equation on Nontrapping Asymptotically Conic Manifolds	2005	Andrew Hassell TERENCE TAO Jared Wunsch
+	On the blowing up of solutions to the Cauchy problem for nonlinear Schrödinger equations	1977	Robert T. Glassey
+ PDF Chat	On the asymptotic behavior of large radial data for a focusing non-linear Schrödinger equation	2004	Terence Tao