Global well-posedness and polynomial bounds for the defocusing L 2-critical nonlinear Schrodinger equation in ℝ

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

Research output: Contribution to journalArticlepeer-review

Abstract

We prove global well-posedness for low regularity data for the one dimensional quintic defocusing nonlinear Schrodinger equation. Precisely we show that a unique and global solution exists for initial data in the Sobolev space Hs(ℝ) for any [image omitted]. This improves the result in [25], where global well-posedness was established for any [image omitted]. We use the I-method to take advantage of the conservation laws of the equation. The new ingredient in our proof is an interaction Morawetz estimate for the smoothed out solution Iu. As a byproduct of our proof we also obtain that the Hs norm of the solution obeys polynomial-in-time bounds.

Original languageEnglish (US)
Pages (from-to)1395-1429
Number of pages35
JournalCommunications in Partial Differential Equations
Volume33
Issue number8
DOIs
StatePublished - Aug 26 2008
Externally publishedYes

Keywords

  • Global well-posedness
  • Morawetz estimates
  • Schrodinger equation

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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