Global existence and scattering for rough solutions of a nonlinear Schroedinger equation on R^3
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We prove global existence and scattering for the defocusing, cubic nonlinear Schrödinger equation in $H^s(\rr^3)$ for $s > {4/5}$. The main new estimate in the argument is a Morawetz-type inequality for the solution $ϕ$. This estimate bounds $\|ϕ(x,t)\|_{L^4_{x,t}(\rr^3 \times \rr)}$, whereas the well-known Morawetz-type estimate of Lin-Strauss controls $\int_0^{\infty}\int_{\rr^3}\frac{(ϕ(x,t))^4}{|x|} dx dt
Final version, to appear in Communications on Pure and Applied Mathematics: typos fixed, some expository remarks and references added, referee's suggestions incorporated
Final version, to appear in Communications on Pure and Applied Mathematics: typos fixed, some expository remarks and references added, referee's suggestions incorporated