Energy critical NLS in two space dimensions

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

Research output: Contribution to journalArticlepeer-review

Abstract

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.

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

Keywords

  • Energy critical
  • Nonlinear Schrödinger equation
  • Well-posedness

ASJC Scopus subject areas

  • Analysis
  • Mathematics(all)

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