Inviscid limit for the derivative Ginzburg-Landau equation with small data in modulation and Sobolev spaces

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• 作者：Lijia Han^a ; ^c ; ^{hljmath@gmail.com} ; Baoxiang Wang^b ; ^{wbx@math.pku.edu.cn} ; Boling Guo^a ; ^{gbl@mail.iapcm.ac.cn}
• 关键词：Derivative Ginzburg&ndash ; Landau equation ; Derivative Schrö ; dinger equation ; Inviscid limit ; Modulation spaces ; Frequency-uniform localization method
• 刊名：Applied and Computational Harmonic Analysis
• 出版年：2012
• 出版时间：March 2012
• 年：2012
• 卷：32
• 期：2
• 页码：197-222
• 全文大小：361 K

文摘

Applying the frequency-uniform decomposition technique, we study the Cauchy problem for derivative Ginzburg-Landau equation , where , are complex constant vectors, , . For , we show that it is uniformly global well posed for all if initial data in modulation space and Sobolev spaces () and is small enough. Moreover, we show that its solution will converge to that of the derivative Schr?dinger equation in if and in or with . For , we obtain the local well-posedness results and inviscid limit with the Cauchy data in () and .