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

Léger, Tristan

doi:10.2140/apde.2021.14.1977

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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

DOI: 10.2140/apde.2021.14.1977

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

Vol. 14, No. 7, 2021