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Global well-posedness and scattering for the defocusing, $L^{2}$-critical nonlinear Schrödinger equation when $d ≥3$

Global well-posedness and scattering for the defocusing, $L^{2}$-critical nonlinear Schrödinger equation when $d ≥3$

In this paper we prove that the defocusing, $d$-dimensional mass critical nonlinear Schrödinger initial value problem is globally well-posed and solutions scatter for $u_{0} \in L^{2}(\mathbf {R}^{d})$, $d \geq 3$. To do this, we will prove a frequency localized interaction Morawetz estimate similar to the estimate made by Colliander, Keel, …