Global well-posedness and scattering for the derivative nonlinear Schrödinger equation with small rough data
Wang Baoxiang
LMAM, School of Mathematical Sciences, Peking University, Beijing 100871, ChinaHan Lijia
LMAM, School of Mathematical Sciences, Peking University, Beijing 100871, ChinaHuang Chunyan
LMAM, School of Mathematical Sciences, Peking University, Beijing 100871, China
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Abstract
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 . Noticing that are optimal inclusions, we have shown the global well posedness of DNLS with a class of rough data. As a by-product, the existence of the scattering operators in modulation spaces with small data is also obtained.
Cite this article
Wang Baoxiang, Han Lijia, Huang Chunyan, Global well-posedness and scattering for the derivative nonlinear Schrödinger equation with small rough data. Ann. Inst. H. Poincaré Anal. Non Linéaire 26 (2009), no. 6, pp. 2253–2281
DOI 10.1016/J.ANIHPC.2009.03.004