Global well posedness and scattering for the elliptic and non-elliptic derivative nonlinear Schrodinger equations with small data

2008/03/18 by Baoxiang Wang, Wang, Baoxiang · 2 citations
Mathematics · #35Q55 #Advanced Harmonic Analysis Research #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Mathematical Analysis and Transform Methods #math.AP #msc:35Q55

paper · pdf · doi:10.48550/arxiv.0803.2634

43 pages

arxiv created 2008/03/18 · openalex publication_date 2008/03/18 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the Cauchy problem for the generalized elliptic and non-elliptic derivative nonlinear Schrodinger equations, the existence of the scattering operators and the global well posedness of solutions with small data in Besov spaces and in modulation spaces are obtained. In one spatial dimension, we get the sharp well posedness result with small data in critical homogeneous Besov spaces. As a by-product, the existence of the scattering operators with small data is also shown. In order to show these results, the global versions of the estimates for the maximal functions on the elliptic and non-elliptic Schrodinger groups are established.

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• Sharp global well-posedness for non-elliptic derivative Schrödinger equations with small rough data
• Global well-posedness and scattering for Derivative Schrödinger equation

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