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

Corcho, A.; Linares, F.

doi:10.1090/S0002-9947-07-04239-0

Well-posedness for the Schrödinger-Korteweg-de Vries system
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by A. J. Corcho and F. Linares PDF

Trans. Amer. Math. Soc. 359 (2007), 4089-4106 Request permission

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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