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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 3 4 + . This result implies in particular the global well-posedness in the energy space H 1 (R) × H 1 (R). Both results considerably improve the previous ones by 4089 License or copyright restrictions may apply to redistribution; see http://www.ams.org/journal-terms-of-use 4090doi:10.1090/s0002-9947-07-04239-0 fatcat:xo4renzcundi7mtjpv65izvndq