Vol. 6, No. 8, 2013

Download this article
Download this article For screen
For printing
Recent Issues

Volume 10
Issue 7, 1539–1791
Issue 6, 1285–1538
Issue 5, 1017–1284
Issue 4, 757–1015
Issue 3, 513–756
Issue 2, 253–512
Issue 1, 1–252

Volume 9, 8 issues

Volume 8, 8 issues

Volume 7, 8 issues

Volume 6, 8 issues

Volume 5, 5 issues

Volume 4, 5 issues

Volume 3, 4 issues

Volume 2, 3 issues

Volume 1, 3 issues

The Journal
About the Cover
Editorial Board
Editors’ Interests
About the Journal
Scientific Advantages
Submission Guidelines
Submission Form
Editorial Login
Author Index
To Appear
ISSN: 1948-206X (e-only)
ISSN: 2157-5045 (print)
Global well-posedness for the nonlinear Schrödinger equation with derivative in energy space

Yifei Wu

Vol. 6 (2013), No. 8, 1989–2002

In this paper, we prove that there exists some small ε > 0 such that the derivative nonlinear Schrödinger equation (DNLS) is globally well-posed in the energy space, provided that the initial data u0 H1() satisfies u0L2 < 2π + ε. This result shows us that there are no blow-up solutions whose masses slightly exceed 2π, even if their energies are negative. This phenomenon is much different from the behavior of the nonlinear Schrödinger equation with critical nonlinearity. The technique used is a variational argument together with the momentum conservation law. Further, for the DNLS on the half-line +, we show the blow-up for the solution with negative energy.

nonlinear Schrödinger equation with derivative, global well-posedness, blow-up, half-line
Mathematical Subject Classification 2010
Primary: 35Q55
Secondary: 35A01, 35B44
Received: 9 March 2013
Revised: 11 September 2013
Accepted: 4 October 2013
Published: 20 April 2014
Yifei Wu
School of Mathematical Science
Beijing Normal University
Laboratory of Mathematics and Complex Systems
Ministry of Education
Beijing, 100875