#### Vol. 10, No. 5, 2017

 Recent Issues
 The Journal About the Journal Editorial Board Editors’ Interests Subscriptions Submission Guidelines Submission Form Policies for Authors Ethics Statement ISSN: 1948-206X (e-only) ISSN: 2157-5045 (print) Author Index To Appear Other MSP Journals
A sufficient condition for global existence of solutions to a generalized derivative nonlinear Schr&ouml;dinger equation

### Noriyoshi Fukaya, Masayuki Hayashi and Takahisa Inui

Vol. 10 (2017), No. 5, 1149–1167
##### Abstract

We give a sufficient condition for global existence of the solutions to a generalized derivative nonlinear Schrödinger equation (gDNLS) by a variational argument. The variational argument is applicable to a cubic derivative nonlinear Schrödinger equation (DNLS). For (DNLS), Wu (2015) proved that the solution with the initial data ${u}_{0}$ is global if $\parallel {u}_{0}{\parallel }_{{L}^{2}}^{2}<4\pi$ by the sharp Gagliardo–Nirenberg inequality. The variational argument gives us another proof of the global existence for (DNLS). Moreover, by the variational argument, we can show that the solution to (DNLS) is global if the initial data ${u}_{0}$ satisfies $\parallel {u}_{0}{\parallel }_{{L}^{2}}^{2}=4\pi$ and the momentum $P\left({u}_{0}\right)$ is negative.

However, your active subscription may be available on Project Euclid at
https://projecteuclid.org/apde

We have not been able to recognize your IP address 44.192.65.228 as that of a subscriber to this journal.
Online access to the content of recent issues is by subscription, or purchase of single articles.

or by using our contact form.