Global well-posedness on the derivative nonlinear Schrödinger equation

Wu, Yifei

doi:10.2140/apde.2015.8.1101

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Global well-posedness on the derivative nonlinear Schrödinger equation

Yifei Wu

Vol. 8 (2015), No. 5, 1101–1112

DOI: 10.2140/apde.2015.8.1101

Abstract

As a continuation of our previous work, we consider the global well-posedness for the derivative nonlinear Schrödinger equation. We prove that it is globally well posed in the energy space, provided that the initial data $u_{0} \in H^{1} (ℝ)$ with $∥ u_{0} ∥_{L^{2}} < 2 \sqrt{π}$ .

Keywords

nonlinear Schrödinger equation with derivative, global well-posedness, energy space

Mathematical Subject Classification 2010

Primary: 35Q55

Secondary: 35A01

Milestones

Received: 14 September 2014

Revised: 4 February 2015

Accepted: 6 March 2015

Published: 28 July 2015

Authors

Yifei Wu
Center for Applied Mathematics Tianjin University Tianjin 300072 China	School of Mathematical Sciences Laboratory of Mathematics and Complex Systems Beijing Normal University Ministry of Education Beijing, 100875 China

Vol. 8, No. 5, 2015