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As a continuation of the previous work \cite{Wu}, we consider the globalwell-posedness for the derivative nonlinear Schr\"odinger equation. We provethat it is globally well-posed in energy space, provided that the initial data$u_0\in H^1(\mathbb{R})$ with $\|u_0\|_{L^2}< 2\sqrt{\pi}$.

Global well-posedness on the derivative nonlinear Schr\"odinger equation revisited