Abstract
We consider non-gauge-invariant cubic nonlinear Schrödinger equations in one space dimension. We show that initial data of size ϵ in a weighted Sobolev space lead to solutions with sharp L∞x decay up to time exp(Cϵ-2). We also exhibit norm growth beyond this time for a specific choice of nonlinearity.
Original language | English (US) |
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Pages (from-to) | 2077-2102 |
Number of pages | 26 |
Journal | Discrete and Continuous Dynamical Systems- Series A |
Volume | 37 |
Issue number | 4 |
DOIs | |
State | Published - Apr 2017 |
All Science Journal Classification (ASJC) codes
- Analysis
- Discrete Mathematics and Combinatorics
- Applied Mathematics
Keywords
- Almost global existence
- Cubic NLS
- Method of space-time resonances