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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 |
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Vol. 14 (2021), No. 7, 2225–2268
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Abstract |
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We consider the Cauchy initial value problem for the defocusing quintic nonlinear Schrödinger equation in two dimensions with general data in the critical space . We show that if a solution remains bounded in in its maximal interval of existence, then the interval is infinite and the solution scatters. |
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Keywords
NLS, scattering, Morawetz inequality,
concentration-compactness
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Mathematical Subject Classification 2010
Primary: 35Q55
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Milestones
Received: 30 September 2019
Revised: 21 April 2020
Accepted: 31 July 2020
Published: 10 November 2021
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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 |
