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Well-posedness for the Schrödinger-Korteweg-de Vries system

Authors: A. J. Corcho and F. Linares
Journal: Trans. Amer. Math. Soc. 359 (2007), 4089-4106
MSC (2000): Primary 35Q55, 35Q60, 35B65
Published electronically: April 11, 2007
MathSciNet review: 2309177
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Abstract: We study well-posedness of the Cauchy problem associated to the Schrödinger-Korteweg-de Vries system. We obtain local well-posedness for weak initial data, where the best result obtained is for data in the Sobolev space $ L^2({\mathbb{R}})\times H^{-\tfrac{3}{4}+} $. This result implies in particular the global well-posedness in the energy space $ H^1({\mathbb{R}})\times H^1({\mathbb{R}})$. Both results considerably improve the previous ones by Bekiranov, Ogawa and Ponce (1997), Guo and Miao (1999), and Tsutsumi (1993).

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Additional Information

A. J. Corcho
Affiliation: Departamento de Matemática, Universidade Federal de Alagoas, Campus A. C. Simões, Tabuleiro dos Martins, Maceió-AL, 57072-970, Brazil

F. Linares
Affiliation: IMPA, Estrada Dona Castorina 110, Rio de Janeiro, 22460–320, Brazil

Keywords: Well-posedness, Schr\"odinger-Korteweg-de Vries system
Received by editor(s): February 4, 2005
Published electronically: April 11, 2007
Additional Notes: The first author was supported by CNPq and FAPEAL, Brazil
The second author was partially supported by CNPq, Brazil
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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