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arXiv · 2408.10028

Sharp local well-posedness for the Schr\"odinger-Korteweg-de Vries system

Simão Correia·Felipe Linares·Jorge Drumond Silva
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Abstract

We prove a sharp local existence result for the Schr\"odinger-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 \textit{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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Simão Correia, Felipe Linares, Jorge Drumond Silva. 2024-08-19. Sharp local well-posedness for the Schr\"odinger-Korteweg-de Vries system. https://arxiv.org/abs/2408.10028

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