#### Vol. 14, No. 7, 2021

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Global well-posedness and scattering for the defocusing $\dot{H}^{1/2}$-critical nonlinear Schrödinger equation in $\mathbb{R}^2$

### Xueying Yu

Vol. 14 (2021), No. 7, 2225–2268
##### Abstract

We consider the Cauchy initial value problem for the defocusing quintic nonlinear Schrödinger equation in two dimensions with general data in the critical space ${Ḣ}^{1∕2}\left({ℝ}^{2}\right)$. We show that if a solution remains bounded in ${Ḣ}^{1∕2}\left({ℝ}^{2}\right)$ in its maximal interval of existence, then the interval is infinite and the solution scatters.

##### Keywords
NLS, scattering, Morawetz inequality, concentration-compactness
Primary: 35Q55