Global Smooth Effects and Well-Posedness for the Derivative Nonlinear Schrödinger Equation with Small Rough Data

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dc.creatorBaoxiang, Wang
dc.creatorLijia, Han
dc.creatorChunyan, Huang
dc.date2008-08-22
dc.date2008-12-09
dc.date.accessioned2026-07-07T12:09:56Z
dc.date.available2026-07-07T12:09:56Z
dc.description\rm We obtain the global smooth effects for the solutions of the linear Schrödinger equation in anisotropic Lebesgue spaces. Applying these estimates, we study the Cauchy problem for the generalized elliptical and non-elliptical derivative nonlinear Schrödinger equations (DNLS) and get the global well posedness of solutions with small data in modulation spaces $M^{3/2}_{2,1}(\mathbb{R}^n)$. Noticing that $H^{\tilde{s}} \subset M^s_{2,1}$ $(\tilde{s}-s>n/2)$ is an optimal inclusion, we have shown the global well posedness of DNLS with a class of very rough data.
dc.description42 Pages
dc.identifierhttps://arxiv.org/abs/0808.3098
dc.identifierhttp://arxiv.org/abs/0808.3098
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/209796
dc.subjectAnalysis of PDEs
dc.subjectFunctional Analysis
dc.subject35Q55
dc.titleGlobal Smooth Effects and Well-Posedness for the Derivative Nonlinear Schrödinger Equation with Small Rough Data
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