Well-posedness for the Schrödinger-Korteweg-de Vries system
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- by A. J. Corcho and F. Linares PDF
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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).References
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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
- Email: adan@mat.ufal.br
- F. Linares
- Affiliation: IMPA, Estrada Dona Castorina 110, Rio de Janeiro, 22460–320, Brazil
- MR Author ID: 343833
- Email: linares@impa.br
- 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 - © Copyright 2007
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 359 (2007), 4089-4106
- MSC (2000): Primary 35Q55, 35Q60, 35B65
- DOI: https://doi.org/10.1090/S0002-9947-07-04239-0
- MathSciNet review: 2309177