Global well-posedness for the derivative nonlinear Schrödinger equation in $H^{\frac 12} (\mathbb{R} )$

Zihua Guo; Yifei Wu

doi:10.3934/dcds.2017010

Article Contents

2017, Volume 37, Issue 1: 257-264. Doi: 10.3934/dcds.2017010

This issue Previous Article Oscillatory orbits in the restricted elliptic planar three body problem Next Article Liouville theorems for stable solutions of the weighted Lane-Emden system

Global well-posedness for the derivative nonlinear Schrödinger equation in $H^{\frac 12} (\mathbb{R} )$

Zihua Guo^1, , and
Yifei Wu^2,

1.
School of Mathematical Sciences, Monash University, VIC 3800, Australia
2.
Center for Applied Mathematics, Tianjin University, Tianjin 300072, China

* Corresponding author: zihua.guo@monash.edu
* Corresponding author: zihua.guo@monash.edu

Received: April 2016

Revised: June 2016

Published: September 2017

The second author is supported by NSFC grant 11571118.

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Abstract

We prove that the derivative nonlinear Schrödinger equation is globally well-posed in $H^{\frac 12} (\mathbb{R} )$ when the mass of initial data is strictly less than 4π.

Keywords:

Nonlinear Schrödinger equation with derivative,
global well-posedness,
low regularity.

Mathematics Subject Classification: Primary:35Q55;Secondary:35A01.

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