Improved almost Morawetz estimates for the cubic nonlinear Schrodinger equation

摘要

We prove global well-posedness for the cubic, defocusing, nonlinearSchr{\"o}dinger equation on $\mathbf{R}^{2}$ with data $u_{0} \inH^{s}(\mathbf{R}^{2})$, $s > 1/4$. We accomplish this by improving the almostMorawetz estimates in [9].