Scattering Criteria for the Three-Dimensional Focusing Energy-Critical Generalized Hartree Equation
Pang-Hung Chung, Akidul Haque, Dan Han
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 \(L2\)-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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