Abstract
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.
| Original language | English |
|---|---|
| Pages (from-to) | 1389-1405 |
| Number of pages | 17 |
| Journal | Discrete and Continuous Dynamical Systems- Series A |
| Volume | 33 |
| Issue number | 4 |
| DOIs | |
| Publication status | Published - 2013 Apr 1 |
Keywords
- Angular regularity
- Critical nonlinearity below L
- Global well-posedness
- Hartree equations
- Weighted Strichartz estimate
ASJC Scopus subject areas
- Analysis
- Discrete Mathematics and Combinatorics
- Applied Mathematics
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Cho, Y., Hwang, G., & Ozawa, T. (2013). Global well-posedness of critical nonlinear Schrödinger equations below L2. Discrete and Continuous Dynamical Systems- Series A, 33(4), 1389-1405. https://doi.org/10.3934/dcds.2013.33.1389