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arXiv · 2411.10977

Local well-posedness for the Schr\"{o}dinger-KdV system in $H^{s_1}\times H^{s_2}$, II

Yingzhe Ban·Jie Chen·Ying Zhang
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Abstract

In this paper, we continue the study of the local well-posedness theory for the Schr\"{o}dinger-KdV system in the Sobolev space $H^{s_1}\times H^{s_2}$. We show the local well-posedness in $H^{-3/16}\times H^{-3/4}$ for $\beta = 0$. Combining our work \cite{banchenzhang}, we also have the local well-posedness for $\max\{-3/4,s_1-3\}\leq s_2\leq \min\{4s_1,s_1+2\}$. The result is sharp by using the contraction mapping argument.

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Yingzhe Ban, Jie Chen, Ying Zhang. 2024-11-17. Local well-posedness for the Schr\"{o}dinger-KdV system in $H^{s_1}\times H^{s_2}$, II. https://arxiv.org/abs/2411.10977

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