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摘要
We prove global well-posedness for the L-2-critical cubic defocusing nonlinear Schrodinger equation on R-2 with data u(0) is an element of H-s (R-2) for s > 1/3. The proof combines a priori Morawetz estimates obtained in [4] and the improved almost conservation law obtained in [6]. There are two technical difficulties. The first one is to estimate the variation of the improved almost conservation law on intervals given in terms of Strichartz spaces rather than in terms of X-s,X-b spaces. The second one is to control the error of the a priori Morawetz estimates on an arbitrary large time interval, which is performed by a bootstrap via a double layer in time decomposition.
- 出版日期2011-3
