Scattering and blow up for the two-dimensional focusing quintic nonlinear Schrödinger equation

Cristi Guevara, Fernando Carreon

Type: Other

Publication Date: 2012-01-01

Citations: 1

DOI: https://doi.org/10.1090/conm/581/11490

Abstract

Using the concentration-compactness method and the localized virial type arguments, we study the behavior of H 1 solutions to the focusing quintic NLS in R 2 , namely,Denoting by M [u] and E[u], the mass and energy of a solution u, respectively, and Q the ground state solution to -Q+∆Q+|Q| 4 Q = 0, and assumingwe characterize the threshold for global versus finite time existence.Moreover, we show scattering for global existing time solutions and finite or "weak" blow up for the complement region.This work is in the spirit of [KM06] and [DHR08, HR08a, HR10].

Locations

Contemporary mathematics - American Mathematical Society - View
arXiv (Cornell University) - View - PDF

Similar Works

Action	Title	Year	Authors
+ PDF Chat	Scattering and Blow up for the Two Dimensional Focusing Quintic Nonlinear Schr\"odinger Equation	2012	Cristi Guevara Fernando Carreon
+	Mass Concentration Phenomenon for the Quintic Nonlinear Schrödinger Equation in One Dimension	2006	Nikolaos Tzirakis
+ PDF Chat	Mass Concentration Phenomenon for the Quintic Nonlinear Schrödinger Equation in One Dimension	2006	Nikolaos Tzirakis
+	On the Focusing Energy-Critical 3D Quintic Inhomogeneous NLS	2020	Yonggeun Cho Kiyeon Lee
+ PDF Chat	Global Behavior of Finite Energy Solutions to the d-Dimensional Focusing Nonlinear Schrodinger Equation	2013	Cristi Guevara
+	Recent Advances in Harmonic Analysis and Partial Differential Equations	2012	Andrea R. Nahmod Christopher D. Sogge Xiaoyi Zhang Shijun Zheng
+	Global existence, scattering and blow-up for the focusing NLS on the hyperbolic space	2014	Valeria Banica Thomas Duyckaerts
+	Characterization of minimal-mass blowup solutions to the focusing mass-critical NLS	2008	Rowan Killip Dong Li Monica Vişan Xiaoyi Zhang
+	Blow up and scattering criteria above the threshold for the focusing inhomogeneous nonlinear Schr\"odinger equation	2020	Luccas Campos Mykael Cardoso
+	Global dynamics below the ground states for NLS under partial harmonic confinement	2020	Alex H. Ardila Rémi Carles
+	Global dynamics below the ground states for NLS under partial harmonic confinement	2020	Alex H. Ardila Rémi Carles
+	Blow up and scattering criteria above the threshold for the focusing inhomogeneous nonlinear Schrödinger equation	2020	Luccas Campos Mykael Cardoso
+	Scattering for the Radial Focusing Inhomogeneous NLS Equation in Higher Dimensions	2019	Luiz Gustavo Farah Carlos M. Guzmán
+ PDF Chat	Going Beyond the Threshold: Scattering and Blow-up in the Focusing NLS Equation	2014	Thomas Duyckaerts Svetlana Roudenko
+	Long-time behavior of solutions to nonlinear Schrödinger-type equations	2019	Luccas Campos
+	Global existence, scattering and blow-up for the focusing NLS on the hyperbolic space	2014	Valeria Banica Thomas Duyckaerts
+ PDF Chat	Dynamics of the non-radial energy-critical inhomogeneous NLS	2024	Carlos M. Guzmán Chenbgin Xu
+	The focusing energy-critical nonlinear Schr\	2008	Rowan Killip Monica Vişan
+ PDF Chat	A global compact attractor for high-dimensional defocusing non-linear Schrödinger equations with potential	2008	Terence Tao
+	On the GWP of focusing energy-ciritical inhomogeneous NLS	2019	Yonggeun Cho Seokchang Hong Kiyeon Lee

Works That Cite This (1)

Action	Title	Year	Authors
+ PDF Chat	Going Beyond the Threshold: Scattering and Blow-up in the Focusing NLS Equation	2014	Thomas Duyckaerts Svetlana Roudenko

Works Cited by This (14)

Action	Title	Year	Authors
+	Nonlinear Dispersive Equations	2006	Terence Tao
+	Nonlinear scattering theory at low energy: Sequel	1981	Walter A. Strauss
+	Convergence of solutions of H-systems or how to blow bubbles	1985	H. Brézis Jean‐Michel Coron
+	Nonlinear scalar field equations, II existence of infinitely many solutions	1983	Henri Berestycki Pierre‐Louis Lions
+ PDF Chat	INHOMOGENEOUS STRICHARTZ ESTIMATES	2005	Damiano Foschi
+	Averaged description of wave beams in linear and nonlinear media (the method of moments)	1971	S. N. Vlasov V. A. Petrishchev V. I. Talanov
+	Oscillations and Concentration Effects in Semilinear Dispersive Wave Equations	1996	Patrick Gérard
+	Nonlinear scattering theory at low energy	1981	Walter A. Strauss
+	Nonlinear scalar field equations, I existence of a ground state	1983	Henri Berestycki P. L. Lions
+ PDF Chat	Endpoint Strichartz estimates	1998	M. Keel Terence Tao