Bootstrapped Morawetz Estimates And Resonant Decomposition For Low Regularity Global Solutions Of Cubic NLS On R^{2}

Abstract

We prove global well-posedness for the L^{2}-critical cubic defocusing nonlinear Schr\"odinger equation on R^{2} with data u_{0} \in H^{s}(R^{2}) for s > {1/3}.