On the ill-posedness of the cubic nonlinear Schrödinger equation on the circle

Tadahiro Oh*, Yuzhao Wang

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)
32 Downloads (Pure)

Abstract

In this note, we consider the ill-posedness issue for the cubic nonlinear Schrödinger equation (NLS)on the circle. In particular, adapting the argument by Christ-Colliander-Tao [14] to the periodic setting, we exhibit a norm inflation phenomenon for both the usual cubic NLS and the Wick ordered cubic NLS for s ≤ scrit := − ½ . We also discuss norm inflation phenomena for general cubic fractional NLS on the circle.

Original languageEnglish
Pages (from-to)53-84
Number of pages32
JournalAnalele Stiintifice ale Universitatii Al I Cuza din Iasi - Matematica
Volume64
Issue number1
Publication statusPublished - 1 Jan 2018

Keywords

  • Ill-posedness
  • Nonlinear Schrödinger equation
  • Norm inflation

ASJC Scopus subject areas

  • Mathematics(all)

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