Global well-posedness on the derivative nonlinear Schrödinger equation

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 $u_0\in H^1\left(ℝ\right)$ with $\parallel u_0{\parallel }_{L^2}<2\sqrt{\pi }$.