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 language | English |
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Pages (from-to) | 53-84 |
Number of pages | 32 |
Journal | Analele Stiintifice ale Universitatii Al I Cuza din Iasi - Matematica |
Volume | 64 |
Issue number | 1 |
Publication status | Published - 1 Jan 2018 |
Keywords
- Ill-posedness
- Nonlinear Schrödinger equation
- Norm inflation
ASJC Scopus subject areas
- General Mathematics