Improved almost Morawetz estimates for the cubic nonlinear Schrodinger equation

Abstract

We prove global well-posedness for the cubic, defocusing, nonlinear Schr{ö}dinger equation on ${\mathbf{R}}^2$ with data $u_0\in H^s({\mathbf{R}}^2)$, $s>1/4$. We accomplish this by improving the almost Morawetz estimates in [9].

20 pages