Global well-posedness for the L2 critical nonlinear Schrödinger equation in higher dimensions

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

Research output: Contribution to journalArticlepeer-review

Abstract

The initial value problem for the L2 critical semilinear Schrödinger equation in ℝ,n, n ≥ 3 is considered. We show that the problem is globally well posed in Hs(ℝ n) when 1 > s > & √7-1/3 for n = 3, and when 1 > s > -(n-2)+√(n-2)2+8(n-2)/4 for n > 4 We use the "I-method" combined with a local in time Morawetz estimate.

Original languageEnglish (US)
Pages (from-to)1023-1041
Number of pages19
JournalCommunications on Pure and Applied Analysis
Volume6
Issue number4
DOIs
StatePublished - Dec 2007

Keywords

  • Global well-posedness
  • I-method
  • Morawetz estimates
  • Schrödinger equations

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

Fingerprint Dive into the research topics of 'Global well-posedness for the L<sup>2</sup> critical nonlinear Schrödinger equation in higher dimensions'. Together they form a unique fingerprint.

Cite this