Global well-posedness of critical nonlinear Schrödinger equations below L2

Yonggeun Cho, Gyeongha Hwang, Tohru Ozawa

研究成果: Article査読

8 被引用数 (Scopus)

抄録

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.

本文言語English
ページ(範囲)1389-1405
ページ数17
ジャーナルDiscrete and Continuous Dynamical Systems- Series A
33
4
DOI
出版ステータスPublished - 2013 4

ASJC Scopus subject areas

  • Analysis
  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

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