Global existence and scattering for rough solutions of a nonlinear Schroedinger equation on R^3

. We prove global existence and scattering for the defocusing, cubic nonlinear Schr¨odinger equation in H s ( R 3 ) for s > 45 . The main new estimate in the argument is a Morawetz-type inequality for the solution φ . This estimate bounds k φ ( x,t ) k L 4 x,t ( R 3 × R ) , whereas the well-known Morawetz-type estimate of Lin-Strauss controls