Vol. 14, No. 7, 2021

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Global existence and scattering for quadratic NLS with potential in three dimensions

Tristan Léger

Vol. 14 (2021), No. 7, 1977–2046
Abstract

We study the asymptotic behavior of a quadratic NLS equation with small, time-dependent potential and small spatially localized initial data. We prove global existence and scattering of solutions. The two main ingredients of the proof are the space-time resonance method and the boundedness of wave operators for the linear Schrödinger equation with potential.

Keywords
space-time resonances, Schrödinger equation
Mathematical Subject Classification 2010
Primary: 35Q55
Milestones
Received: 25 April 2018
Revised: 2 April 2020
Accepted: 6 May 2020
Published: 10 November 2021
Authors
Tristan Léger
Courant Institute of Mathematical Sciences
New York University
New York, NY
United States