Improved interaction Morawetz inequalities for the cubic nonlinear Schrödinger equation on ${\mathbb{R}}^2$

J. Colliander, M. Grillakis, N. Tzirakis

We prove global well-posedness for low regularity data for the $L^2-critical$ defocusing nonlinear Schrödinger equation (NLS) in 2d. More precisely we show that a global solution e…