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Bootstrapped Morawetz estimates and resonant decomposition for low regularity global solutions of cubic NLS on $R^2$
We prove global well-posedness for the $L^2$-critical cubic defocusing nonlinear Schrödinger equation on $R^2$ with data $u_0 \in H^s(R^2)$ for $ s > \frac{1}{3}$. The proof combines <em>a priori</em> Morawetz estimates obtained in [4] and the improved almost conservation law obtained in [6]. There are two technical difficulties. The first …