On the blow up phenomenon of the critical nonlinear Schrödinger equation

Sahbi Keraani

Type: Article

Publication Date: 2005-12-02

Citations: 121

DOI: https://doi.org/10.1016/j.jfa.2005.10.005

View Publication

Locations

HAL (Le Centre pour la Communication Scientifique Directe) - View
Journal of Functional Analysis - View

Similar Works

Action	Title	Year	Authors
+	Blowup for the Damped $L^{2}$-Critical Nonlinear Schrödinger Equation	2011	Mohamad Darwich
+ PDF Chat	Blow-up for the damped $L^{2}$-critical nonlinear Schrödinger equation	2012	Mohamad Darwich
+ PDF Chat	Blowup for the Damped $L^{2}$-Critical Nonlinear Schrödinger Equation.	2012	Mohamad Darwich
+	L2 concentration of blow-up solutions for the nonlinear Schrödinger equation with critical power nonlinearity	1990	Frank Merle Yoshio Tsutsumi
+ PDF Chat	On the blow up phenomenon for the critical nonlinear Schrödinger equation in 1D	2001	Galina Perelman
+	Minimal mass blow-up solutions for nonlinear Schrödinger equations with a potential	2020	Naoki Matsui
+ PDF Chat	Minimal mass blow-up solutions for nonlinear Schrödinger equations with a potential	2023	Naoki Matsui
+ PDF Chat	On blow-up solutions to the focusing mass-critical nonlinear fractional Schrödinger equation	2018	Van Duong Dinh
+	CONCENTRATION PHENOMENON FOR THE L<sup>2</sup> CRITICAL AND SUPER CRITICAL NONLINEAR SCHRÖDINGER EQUATIONS IN ENERGY SPACES	2006	Baoxiang Wang
+ PDF Chat	The blow-up dynamic and upper bound on the blow-up rate for critical nonlinear Schrödinger equation	2005	Frank Merle Pierre Raphaël
+	Remarks on the Blowup for the $L^2$‐Critical Nonlinear Schrödinger Equations	2006	Taoufik Hmidi Sahbi Keraani
+	On Blowup solutions to the focusing mass-critical nonlinear fractional Schrödinger equation	2018	Van Duong Dinh
+	On the blowup theory for the critical nonlinear Schrödinger equations	2005	Sahbi Keraani
+ PDF Chat	Limiting profiles of blow-up solutions of the nonlinear Sehrödinger equation with critical power nonlinearity	1997	Hayato Nawa
+	Numerical verification of a spectral property related to blow-up for the critical nonlinear Schrodinger equation	2005	Gadi Fibich Franck Merle Pierre Raphaël
+	Profiles and Quantization of the Blow Up Mass for Critical Nonlinear Schr�dinger Equation	2004	Frank Merle Pierre Raphaël
+	Blow-up of Solutions of the Cauchy Problem for a Nonlinear Schrödinger Evolution Equation	2018	Sh. M. Nasibov
+ PDF Chat	On the role of quadratic oscillations in nonlinear Schrödinger equations II. The $L^2$-critical case	2006	Rémi Carles Sahbi Keraani
+ PDF Chat	Minimal-mass blowup solutions of the mass-critical NLS	2008	Terence Tao Monica Vişan Xiaoyi Zhang
+ PDF Chat	Blow-up criteria for linearly damped nonlinear Schrödinger equations	2020	Van Duong Dinh

Works That Cite This (118)

Action	Title	Year	Authors
+ PDF Chat	A smoothing property for the $ L^{2} $-critical NLS equations and an application to blowup theory	2008	Sahbi Keraani Ana Vargas
+ PDF Chat	Scattering for the non-radial inhomogeneous NLS	2021	Changxing Miao Jason Murphy Jiqiang Zheng
+	Lyapunov type operators for numerical solutions of PDEs	2008	Anouar Ben Mabrouk Mekki Ayadi
+ PDF Chat	Scattering for the cubic Klein–Gordon equation in two space dimensions	2011	Rowan Killip Betsy Stovall Monica Vişan
+	A pseudoconformal compactification of the nonlinear Schrodinger equation and applications	2009	Terence Tao
+ PDF Chat	Profiles for bounded solutions of dispersive equations, with applications to energy-critical wave and Schrödinger equations	2015	Thomas Duyckaerts Carlos E. Kenig Frank Merle
+	The $L^{2}$ weak sequential convergence of radial mass critical NLS solutions with mass above the ground state	2016	Chenjie Fan
+	Large Outgoing Solutions to Supercritical Wave Equations	2016	Marius Beceanu Avy Soffer
+	Global existence and uniqueness results for weak solutions of the focusing mass-critical non-linear Schrödinger equation	2008	Terence Tao
+	The Riemann-Hilbert approach for the focusing Hirota equation with single and double poles	2021	Xiaofan Zhang Shou‐Fu Tian Jin‐Jie Yang

Works Cited by This (18)

Action	Title	Year	Authors
+	Determination of blow-up solutions with minimal mass for nonlinear Schrödinger equations with critical power	1993	Franck Merle
+	Restrictions of Fourier transforms to quadratic surfaces and decay of solutions of wave equations	1977	Robert S. Strichartz
+	Profile decomposition for the wave equation outside a convex obstacle	2001	Isabelle Gallagher Patrick Gérard
+	Rate of L2 concentration of blow-up solutions for the nonlinear schrödinger equation with critical power	1990	Yoshio Tsutsumi
+	On the structure and formation of singularities in solutions to nonlinear dispersive evolution equations	1986	Michael I. Weinstein
+	On the Defect of Compactness for the Strichartz Estimates of the Schrödinger Equations	2001	Sahbi Keraani
+	Asymptotic and limiting profiles of blowup solutions of the nonlinear Schr�dinger equation with critical power	1999	Hayato Nawa
+	Nonlinear Schr�dinger equations and sharp interpolation estimates	1983	Michael I. Weinstein
+	L2 concentration of blow-up solutions for the nonlinear Schrödinger equation with critical power nonlinearity	1990	Frank Merle Yoshio Tsutsumi
+ PDF Chat	Construction of solutions with exactly k blow-up points for the Schrödinger equation with critical nonlinearity	1990	Frank Merle

Action	Title	Year	Authors
+ PDF Chat	A smoothing property for the \( L^{2} \)-critical NLS equations and an application to blowup theory	2008	Sahbi Keraani Ana Vargas
+ PDF Chat	Scattering for the non-radial inhomogeneous NLS	2021	Changxing Miao Jason Murphy Jiqiang Zheng
+	Lyapunov type operators for numerical solutions of PDEs	2008	Anouar Ben Mabrouk Mekki Ayadi
+ PDF Chat	Scattering for the cubic Klein–Gordon equation in two space dimensions	2011	Rowan Killip Betsy Stovall Monica Vişan
+	A pseudoconformal compactification of the nonlinear Schrodinger equation and applications	2009	Terence Tao
+ PDF Chat	Profiles for bounded solutions of dispersive equations, with applications to energy-critical wave and Schrödinger equations	2015	Thomas Duyckaerts Carlos E. Kenig Frank Merle
+	The $L^{2}$ weak sequential convergence of radial mass critical NLS solutions with mass above the ground state	2016	Chenjie Fan
+	Large Outgoing Solutions to Supercritical Wave Equations	2016	Marius Beceanu Avy Soffer
+	Global existence and uniqueness results for weak solutions of the focusing mass-critical non-linear Schrödinger equation	2008	Terence Tao
+	The Riemann-Hilbert approach for the focusing Hirota equation with single and double poles	2021	Xiaofan Zhang Shou‐Fu Tian Jin‐Jie Yang