Global existence and scattering for rough solutions of a nonlinear Schrödinger equation on ℝ3

We prove global existence and scattering for the defocusing, cubic nonlinear Schrodinger equation in H s (R 3 ) for s > 4 . The main new estimate in the argument is a Morawetz-type inequality for the solution �. This estimate bounds k �(x,t)k L 4(R3×R) , whereas the well-known Morawetz-type estimate of Lin-Strauss controls R 1 0 R R3 (�(x,t))4 |x| dxdt.

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