Sharp local well-posedness for the Schrödinger-Korteweg-de Vries system

We prove a sharp local existence result for the Schrödinger-Korteweg-de Vries system with initial data in $H^k(\mathbb{R})\times H^s(\mathbb{R})$. The proof is based on the concept of $\mathit{\text{integrated-by-parts}}\mathit{\text{strong}}\mathit{\text{solution}}$, which generalizes the classical notion of strong solution, and on frequency-restricted estimates. Moreover, we extend the known global well-posedness result to regularities $k,s>1\mathrm{/}2$.