Global well-posedness and scattering for the defocusing, $L^2$-critical, nonlinear Schr{ö}dinger equation when $d=2$

Abstract

In this paper we prove that the defocusing, cubic nonlinear Schr{ö}dinger initial value problem is globally well-posed and scattering for $u_0\in L^2({\mathbf{R}}^2)$. To do this, we will prove a frequency localized interaction Morawetz estimate similar to the estimate made in \cite{CKSTT4}. Since we are considering an $L^2$ - critical initial value problem we will localize to low frequencies.

75 pages

References in corpus (2)

• Global well-posedness, scattering and blow-up for the energy-critical, focusing, non-linear Schrodinger equation in the radial case
• Well-posedness and scattering for the KP-II equation in a critical space

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