## Global well-posedness on the derivative nonlinear Schrödinger equation.(English)Zbl 1326.35361

Summary: 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 $$u_0\in H^1(\mathbb{R})$$ with $$\|u_0\|_{L^2}< 2\sqrt{\pi}$$.

### MSC:

 35Q55 NLS equations (nonlinear Schrödinger equations) 35A01 Existence problems for PDEs: global existence, local existence, non-existence
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