Abstract: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 $6$.
| Comments: | 14 pages, 2 figures |
| Subjects: | Analysis of PDEs (math.AP) |
| Cite as: | arXiv:2605.25341 [math.AP] |
| (or arXiv:2605.25341v1 [math.AP] for this version) | |
| https://doi.org/10.48550/arXiv.2605.25341 arXiv-issued DOI via DataCite (pending registration) |
From: Seongyeon Kim [view email]
[v1]
Mon, 25 May 2026 01:54:47 UTC (438 KB)
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