Global well-posedness and scattering for Derivative Schr\"{o}dinger equation

TL;DR

This paper establishes global well-posedness and scattering for derivative nonlinear Schrödinger equations in higher dimensions with small initial data in critical Besov spaces, advancing understanding of their long-term behavior.

Contribution

It provides new global well-posedness results and scattering theory for derivative Schrödinger equations in higher dimensions with small initial data.

Findings

Global well-posedness in critical Besov spaces

Scattering results for small initial data

Extension to higher spatial dimensions (n ≥ 2)

Abstract

In this paper we study the Cauchy problem for the elliptic and non-elliptic derivative nonlinear Schr\"odinger equations in higher spatial dimensions ($n\geq 2$) and some global well-posedness results with small initial data in critical Besov spaces $B^s_{2,1}$ are obtained. As by-products, the scattering results with small initial data are also obtained.