Global well-posedness and equicontinuity for mKdV in modulation spaces
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866913910480699392 |
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| author | Haque, Saikatul Killip, Rowan Visan, Monica Zhang, Yunfeng |
| author_facet | Haque, Saikatul Killip, Rowan Visan, Monica Zhang, Yunfeng |
| contents | We establish global well-posedness for both the defocusing and focusing complex-valued modified Korteweg--de Vries equations on the real line in modulation spaces $M_p^{s,2}(\mathbb{R})$, for all $1\leq p<\infty$ and $0\leq s<3/2-1/p$. We will also show that such solutions admit global-in-time bounds in these spaces and that equicontinuous sets of initial data lead to equicontinuous ensembles of orbits. Indeed, such information forms a crucial part of our well-posedness argument. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_05300 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Global well-posedness and equicontinuity for mKdV in modulation spaces Haque, Saikatul Killip, Rowan Visan, Monica Zhang, Yunfeng Analysis of PDEs We establish global well-posedness for both the defocusing and focusing complex-valued modified Korteweg--de Vries equations on the real line in modulation spaces $M_p^{s,2}(\mathbb{R})$, for all $1\leq p<\infty$ and $0\leq s<3/2-1/p$. We will also show that such solutions admit global-in-time bounds in these spaces and that equicontinuous sets of initial data lead to equicontinuous ensembles of orbits. Indeed, such information forms a crucial part of our well-posedness argument. |
| title | Global well-posedness and equicontinuity for mKdV in modulation spaces |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2411.05300 |