Correction to "global well-posedness and polynomial bounds for the defocusing L2-critical nonlinear Schrödinger equation in ℝ"

Daniela de Silva; Nataša Pavlović; Gigliola Staffilani; Nikolaos Tzirakis

doi:10.1080/03605301003717159

Correction to "global well-posedness and polynomial bounds for the defocusing L²-critical nonlinear Schrödinger equation in ℝ"

Daniela de Silva, Nataša Pavlović, Gigliola Staffilani, Nikolaos Tzirakis

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

In this correction we prove that the first modified energy of the quintic Schrödinger equation in 1d has an inverse square decay with respect to a very large frequency parameter N, without using an argument presented in the paper [4] which contains a mistake, see errata [5]. This estimate, when applied to the machinery that was developed in [2], gives global well-posedness for the initial value problem in question for any s > 1/3, as was claimed in [2].

Original language	English (US)
Pages (from-to)	293-303
Number of pages	11
Journal	Communications in Partial Differential Equations
Volume	36
Issue number	2
DOIs	https://doi.org/10.1080/03605301003717159
State	Published - Feb 2011

Keywords

Global well-posedness
Nonlinear Schrödinger equation
Nonlinear dispersive equations

ASJC Scopus subject areas

Analysis
Applied Mathematics

Online availability

10.1080/03605301003717159

Library availability

Discover UIUC Full Text

Cite this

@article{77ad8a47a4764f87a301f5efcc235aea,

title = "Correction to {"}global well-posedness and polynomial bounds for the defocusing L2-critical nonlinear Schr{\"o}dinger equation in ℝ{"}",

abstract = "In this correction we prove that the first modified energy of the quintic Schr{\"o}dinger equation in 1d has an inverse square decay with respect to a very large frequency parameter N, without using an argument presented in the paper [4] which contains a mistake, see errata [5]. This estimate, when applied to the machinery that was developed in [2], gives global well-posedness for the initial value problem in question for any s > 1/3, as was claimed in [2].",

keywords = "Global well-posedness, Nonlinear Schr{\"o}dinger equation, Nonlinear dispersive equations",

author = "{de Silva}, Daniela and Nata{\v s}a Pavlovi{\'c} and Gigliola Staffilani and Nikolaos Tzirakis",

year = "2011",

month = feb,

doi = "10.1080/03605301003717159",

language = "English (US)",

volume = "36",

pages = "293--303",

journal = "Communications in Partial Differential Equations",

issn = "0360-5302",

publisher = "Taylor and Francis Ltd.",

number = "2",

}

TY - JOUR

T1 - Correction to "global well-posedness and polynomial bounds for the defocusing L2-critical nonlinear Schrödinger equation in ℝ"

AU - de Silva, Daniela

AU - Pavlović, Nataša

AU - Staffilani, Gigliola

AU - Tzirakis, Nikolaos

PY - 2011/2

Y1 - 2011/2

N2 - In this correction we prove that the first modified energy of the quintic Schrödinger equation in 1d has an inverse square decay with respect to a very large frequency parameter N, without using an argument presented in the paper [4] which contains a mistake, see errata [5]. This estimate, when applied to the machinery that was developed in [2], gives global well-posedness for the initial value problem in question for any s > 1/3, as was claimed in [2].

AB - In this correction we prove that the first modified energy of the quintic Schrödinger equation in 1d has an inverse square decay with respect to a very large frequency parameter N, without using an argument presented in the paper [4] which contains a mistake, see errata [5]. This estimate, when applied to the machinery that was developed in [2], gives global well-posedness for the initial value problem in question for any s > 1/3, as was claimed in [2].

KW - Global well-posedness

KW - Nonlinear Schrödinger equation

KW - Nonlinear dispersive equations

UR - http://www.scopus.com/inward/record.url?scp=78650294095&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=78650294095&partnerID=8YFLogxK

U2 - 10.1080/03605301003717159

DO - 10.1080/03605301003717159

M3 - Article

AN - SCOPUS:78650294095

VL - 36

SP - 293

EP - 303

JO - Communications in Partial Differential Equations

JF - Communications in Partial Differential Equations

SN - 0360-5302

IS - 2

ER -