Energy critical NLS in two space dimensions

J. Colliander; S. Ibrahim; Mohamed Majdoub; N. Masmoudi

doi:10.1142/S0219891609001927

Energy critical NLS in two space dimensions

J. Colliander, S. Ibrahim, Mohamed Majdoub, N. Masmoudi

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

Abstract

We investigate the initial value problem for a defocusing nonlinear Schrödinger equation with exponential nonlinearity i∂^tu + Δu = u(e^{4π u 2} - 1) in ℝ_t × ℝ_x ². We identify subcritical, critical, and supercritical regimes in the energy space. We establish global well-posedness in the subcritical and critical regimes. Well-posedness fails to hold in the supercritical case.

Original language	English (US)
Pages (from-to)	549-575
Number of pages	27
Journal	Journal of Hyperbolic Differential Equations
Volume	6
Issue number	3
DOIs	https://doi.org/10.1142/S0219891609001927
State	Published - 2009

Keywords

Energy critical
Nonlinear Schrödinger equation
Well-posedness

ASJC Scopus subject areas

Analysis
General Mathematics

Access to Document

10.1142/S0219891609001927

Cite this

@article{e57e54c2fcac4afbb2dcc749e7e120a4,

title = "Energy critical NLS in two space dimensions",

abstract = "We investigate the initial value problem for a defocusing nonlinear Schr{\"o}dinger equation with exponential nonlinearity i∂tu + Δu = u(e4π u 2 - 1) in ℝt × ℝx 2. We identify subcritical, critical, and supercritical regimes in the energy space. We establish global well-posedness in the subcritical and critical regimes. Well-posedness fails to hold in the supercritical case.",

keywords = "Energy critical, Nonlinear Schr{\"o}dinger equation, Well-posedness",

author = "J. Colliander and S. Ibrahim and Mohamed Majdoub and N. Masmoudi",

note = "Funding Information: J. C. is partially supported by N.S.E.R.C. Grant RGPIN 250233-07. S. I. is grateful to the Departments of Mathematics and Statistics at McMaster University and Arizona State University. M. M. is partially supported by the Laboratory of PDE and applications of Faculty of Sciences, Tunis, Tunisia. N. M. is partially supported by an NSF Grant DMS-0703145.",

year = "2009",

doi = "10.1142/S0219891609001927",

language = "English (US)",

volume = "6",

pages = "549--575",

journal = "Journal of Hyperbolic Differential Equations",

issn = "0219-8916",

publisher = "World Scientific Publishing Co. Pte Ltd",

number = "3",

}

TY - JOUR

T1 - Energy critical NLS in two space dimensions

AU - Colliander, J.

AU - Ibrahim, S.

AU - Majdoub, Mohamed

AU - Masmoudi, N.

N1 - Funding Information: J. C. is partially supported by N.S.E.R.C. Grant RGPIN 250233-07. S. I. is grateful to the Departments of Mathematics and Statistics at McMaster University and Arizona State University. M. M. is partially supported by the Laboratory of PDE and applications of Faculty of Sciences, Tunis, Tunisia. N. M. is partially supported by an NSF Grant DMS-0703145.

PY - 2009

Y1 - 2009

N2 - We investigate the initial value problem for a defocusing nonlinear Schrödinger equation with exponential nonlinearity i∂tu + Δu = u(e4π u 2 - 1) in ℝt × ℝx 2. We identify subcritical, critical, and supercritical regimes in the energy space. We establish global well-posedness in the subcritical and critical regimes. Well-posedness fails to hold in the supercritical case.

AB - We investigate the initial value problem for a defocusing nonlinear Schrödinger equation with exponential nonlinearity i∂tu + Δu = u(e4π u 2 - 1) in ℝt × ℝx 2. We identify subcritical, critical, and supercritical regimes in the energy space. We establish global well-posedness in the subcritical and critical regimes. Well-posedness fails to hold in the supercritical case.

KW - Energy critical

KW - Nonlinear Schrödinger equation

KW - Well-posedness

UR - http://www.scopus.com/inward/record.url?scp=70350068902&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=70350068902&partnerID=8YFLogxK

U2 - 10.1142/S0219891609001927

DO - 10.1142/S0219891609001927

M3 - Article

AN - SCOPUS:70350068902

SN - 0219-8916

VL - 6

SP - 549

EP - 575

JO - Journal of Hyperbolic Differential Equations

JF - Journal of Hyperbolic Differential Equations

IS - 3

ER -

Energy critical NLS in two space dimensions

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this