Remarks on the well-posedness of the energy-critical inhomogeneous Hartree equation

Seongyeon Kim; Tarek Saanouni; Ihyeok Seo

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arXiv · 2605.25341

Remarks on the well-posedness of the energy-critical inhomogeneous Hartree equation

Seongyeon Kim·Tarek Saanouni·Ihyeok Seo

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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 $6$.

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Seongyeon Kim, Tarek Saanouni, Ihyeok Seo. 2026-05-25. Remarks on the well-posedness of the energy-critical inhomogeneous Hartree equation. https://arxiv.org/abs/2605.25341

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