Energy critical NLS in two space dimensions

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

Research output: Contribution to journalArticle

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 languageEnglish (US)
Pages (from-to)549-575
Number of pages27
JournalJournal of Hyperbolic Differential Equations
Volume6
Issue number3
DOIs
StatePublished - 2009

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Global Well-posedness
Energy
Well-posedness
Initial Value Problem
Nonlinear Equations
Nonlinearity

Keywords

  • Energy critical
  • Nonlinear Schrödinger equation
  • Well-posedness

ASJC Scopus subject areas

  • Mathematics(all)
  • Analysis

Cite this

Energy critical NLS in two space dimensions. / Colliander, J.; Ibrahim, S.; Majdoub, Mohamed; Masmoudi, N.

In: Journal of Hyperbolic Differential Equations, Vol. 6, No. 3, 2009, p. 549-575.

Research output: Contribution to journalArticle

Colliander, J. ; Ibrahim, S. ; Majdoub, Mohamed ; Masmoudi, N. / Energy critical NLS in two space dimensions. In: Journal of Hyperbolic Differential Equations. 2009 ; Vol. 6, No. 3. pp. 549-575.
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