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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| Online-Zugang: | https://arxiv.org/abs/2410.11266 |
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| _version_ | 1866909534977523712 |
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| author | Chen, Zijun Guo, Zihua Huang, Chunyan |
| author_facet | Chen, Zijun Guo, Zihua Huang, Chunyan |
| contents | We study the \emph{complex-valued} solutions to the Cauchy problem of the modified Korteweg-de Vries equation on the real line. To study the low-regularity problems, we employ a generalized Fourier-Lebesgue space $\widehat{M}^{s}_{r,q}(\mathbb{R})$ that unifies the modulation spaces and the Fourier-Lebesgue spaces. We then prove sharp local well-posedness results in this space by perturbation arguments using $X^{s,b}$-type spaces. Our results improve the previous one in \cite{GV}. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_11266 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Complex-valued solutions of the mKdV equations in generalized Fourier-Lebesgue spaces Chen, Zijun Guo, Zihua Huang, Chunyan Analysis of PDEs We study the \emph{complex-valued} solutions to the Cauchy problem of the modified Korteweg-de Vries equation on the real line. To study the low-regularity problems, we employ a generalized Fourier-Lebesgue space $\widehat{M}^{s}_{r,q}(\mathbb{R})$ that unifies the modulation spaces and the Fourier-Lebesgue spaces. We then prove sharp local well-posedness results in this space by perturbation arguments using $X^{s,b}$-type spaces. Our results improve the previous one in \cite{GV}. |
| title | Complex-valued solutions of the mKdV equations in generalized Fourier-Lebesgue spaces |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2410.11266 |