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We prove global well-posedness for low regularity data for the L2-critical defocusing nonlinear Schrödinger equation (NLS) in 2D. More precisely, we show that a global solution exists for initial data in the Sobolev space Hs(ℝ2) and any $s>\frac25$. This improves the previous result of Fang and Grillakis where global well-posedness was established for any $s\geq\frac12$. We use the I-method to tak...

Improved Interaction Morawetz Inequalities for the Cubic Nonlinear Schrödinger Equation on ℝ2