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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2411.10977 |
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| _version_ | 1866913579798626304 |
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| author | Ban, Yingzhe Chen, Jie Zhang, Ying |
| author_facet | Ban, Yingzhe Chen, Jie Zhang, Ying |
| contents | In this paper, we continue the study of the local well-posedness theory for the Schrödinger-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 $β= 0$. 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_10977 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Local well-posedness for the Schrödinger-KdV system in $H^{s_1}\times H^{s_2}$, II Ban, Yingzhe Chen, Jie Zhang, Ying Analysis of PDEs In this paper, we continue the study of the local well-posedness theory for the Schrödinger-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 $β= 0$. 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. |
| title | Local well-posedness for the Schrödinger-KdV system in $H^{s_1}\times H^{s_2}$, II |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2411.10977 |