Remarks on the well-posedness of the energy-critical inhomogeneous Hartree equation
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866914598949486592 |
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| author | Kim, Seongyeon Saanouni, Tarek Seo, Ihyeok |
| author_facet | Kim, Seongyeon Saanouni, Tarek Seo, Ihyeok |
| contents | We study the energy-critical inhomogeneous Hartree equation in space dimensions three and higher. Previous local well-posedness results left open the parameter regime where the inhomogeneity exponent is small and the Riesz potential exponent is either small or large. We establish local well-posedness for a new range of parameters, thereby substantially filling the remaining open parameter regime. In particular, our result completely resolves the remaining gap in dimensions $5$ and $6$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_25341 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Remarks on the well-posedness of the energy-critical inhomogeneous Hartree equation Kim, Seongyeon Saanouni, Tarek Seo, Ihyeok Analysis of PDEs We study the energy-critical inhomogeneous Hartree equation in space dimensions three and higher. Previous local well-posedness results left open the parameter regime where the inhomogeneity exponent is small and the Riesz potential exponent is either small or large. We establish local well-posedness for a new range of parameters, thereby substantially filling the remaining open parameter regime. In particular, our result completely resolves the remaining gap in dimensions $5$ and $6$. |
| title | Remarks on the well-posedness of the energy-critical inhomogeneous Hartree equation |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2605.25341 |