Global well-posedness for generalized fractional Hartree equations with rough initial data in all dimensions
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866914134179708928 |
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| author | Lu, Yufeng |
| author_facet | Lu, Yufeng |
| contents | We prove the global existence of the solution for fractional Hartree equations with initial data in certain real interpolation spaces between $L^{2}$ and some kinds of new function spaces defined by fractional Schrödinger semigroup, which could imply the global well-posedness of the equation in modulation spaces $M_{p,p'}^{s_{p}}$ for $p$ close to 2 with no smallness condition on initial data, where $s_{p}=(m-2)(1/2-1/p)$. The proof adapts a splitting method inspired by the work of Hyakuna-Tsutsumi, Chaichenets et al. to the modulation spaces and exploits polynomial growth of the fractional Schrödinger semi-group on modulation spaces $M_{p,p'}$ with loss of regularity $s_{p}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_02327 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Global well-posedness for generalized fractional Hartree equations with rough initial data in all dimensions Lu, Yufeng Analysis of PDEs 35R11, 35Q55, 35Q60, 42B37 We prove the global existence of the solution for fractional Hartree equations with initial data in certain real interpolation spaces between $L^{2}$ and some kinds of new function spaces defined by fractional Schrödinger semigroup, which could imply the global well-posedness of the equation in modulation spaces $M_{p,p'}^{s_{p}}$ for $p$ close to 2 with no smallness condition on initial data, where $s_{p}=(m-2)(1/2-1/p)$. The proof adapts a splitting method inspired by the work of Hyakuna-Tsutsumi, Chaichenets et al. to the modulation spaces and exploits polynomial growth of the fractional Schrödinger semi-group on modulation spaces $M_{p,p'}$ with loss of regularity $s_{p}$. |
| title | Global well-posedness for generalized fractional Hartree equations with rough initial data in all dimensions |
| topic | Analysis of PDEs 35R11, 35Q55, 35Q60, 42B37 |
| url | https://arxiv.org/abs/2511.02327 |