On the well-posedness of the Schrodinger-Korteweg-de Vries system

Zihua Guo, Yuzhao Wang

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4 Citations (Scopus)

Abstract

We prove that the Cauchy problem for the Schrodinger-Korteweg-de Vries system is locally well-posed for the initial data belonging to the Sobolev spaces L 2(R)?H -3/4(R), and H s(R)?H -3/4(R) (s>-1/16) for the resonant case. The new ingredient is that we use the F? s-type space, introduced by the first author in Guo (2009) [10], to deal with the KdV part of the system and the coupling terms. In order to overcome the difficulty caused by the lack of scaling invariance, we prove uniform estimates for the multiplier. This result improves the previous one by Corcho and Linares (2007) [6].
Original languageEnglish
Pages (from-to)2500 - 2520
Number of pages21
JournalJournal of Differential Equations
Volume249
Issue number10
DOIs
Publication statusPublished - 2010
Externally publishedYes

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