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arXiv · 2608.06498

Scattering Criteria for the Three-Dimensional Focusing Energy-Critical Generalized Hartree Equation

Pang-Hung Chung·Akidul Haque·Dan Han
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Abstract

Two nonradial scattering criteria are established for the three-dimensional focusing energy-critical generalized Hartree equation below the ground-state threshold, under a bounded-scale concentration--compactness reduction. The first criterion is formulated in terms of fixed-center occupation windows and quantitative bounds on the motion of the concentration center. The second is based on uniform low-frequency \(L^2\)-decay, which yields finite mass, precompactness in the inhomogeneous energy space, a zero-momentum normalization, and sublinear center drift. The proofs combine a localized Hartree virial identity with a critical Hardy--Littlewood--Sobolev estimate controlling the nonlocal tail.

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Pang-Hung Chung, Akidul Haque, Dan Han. 2026-08-10. Scattering Criteria for the Three-Dimensional Focusing Energy-Critical Generalized Hartree Equation. https://arxiv.org/abs/2608.06498

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