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 12(2). We show that if a solution remains bounded in 12(2) in its maximal interval of existence, then the interval is infinite and the solution scatters.

Keywords
NLS, scattering, Morawetz inequality, concentration-compactness
Mathematical Subject Classification 2010
Primary: 35Q55
Milestones
Received: 30 September 2019
Revised: 21 April 2020
Accepted: 31 July 2020
Published: 10 November 2021
Authors
Xueying Yu
Department of Mathematics
Massachusetts Institute of Technology
Cambridge, MA
United States
Department of Mathematics and Statistics
University of Massachusetts
Amherst, MA
United States