Global well-posedness of critical nonlinear Schrödinger equations below L2

Yonggeun Cho, Gyeongha Hwang, Tohru Ozawa

Research output: Contribution to journalArticle

6 Citations (Scopus)

Abstract

The global well-posedness on the Cauchy problem of nonlinear Schrödinger equations (NLS) is studied for a class of critical nonlinearity below L2 in small data setting. We consider Hartree type (HNLS) and inhomogeneous power type NLS (PNLS). Since the critical Sobolev index s c is negative, it is rather difficult to analyze the nonlinear term. To overcome the difficulty we combine weighted Strichartz estimates in polar coordinates with new Duhamel estimates involving angular regularity.

Original languageEnglish
Pages (from-to)1389-1405
Number of pages17
JournalDiscrete and Continuous Dynamical Systems- Series A
Volume33
Issue number4
DOIs
Publication statusPublished - 2013 Apr 1

Keywords

  • Angular regularity
  • Critical nonlinearity below L
  • Global well-posedness
  • Hartree equations
  • Weighted Strichartz estimate

ASJC Scopus subject areas

  • Analysis
  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

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