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 |
|---|---|
| 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
- Mathematics(all)