Global existence and scattering for quadratic NLS with potential in 3D

Abstract

In this article 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.

Revised version, to appear. Scattering statement corrected, presentation improved thanks to referee's comments

References in corpus (2)

• The Euler--Maxwell system for electrons: global solutions in $2D$
• Structure formulas for wave operators under a small scaling invariant condition