We prove a sharp local existence result for the Schr\"odinger-Korteweg-de Vries system with initial data in Hᵏ(R)× Hˢ(R). The proof is based on the concept of integrated-by-parts strong solution, which generalizes the classical notion of strong solution, and on frequency-restricted estimates. Moreover, we extend the known global well-posedness result to regularities $k,s>1/2$.
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Correia et al. (2024) studied this question.
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