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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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