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 |
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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 |
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