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.
|ジャーナル||Discrete and Continuous Dynamical Systems- Series A|
|出版ステータス||Published - 2013 4|
ASJC Scopus subject areas
- Discrete Mathematics and Combinatorics
- Applied Mathematics