AI 中文总结
针对三维聚焦能量临界广义Hartree方程，在基态阈值下建立两个非径向散射准则，通过结合局域Hartree位力恒等式与临界Hardy-Littlewood-Sobolev估计完成证明。
AI 中文摘要
在基态阈值以下，针对三维聚焦能量临界广义Hartree方程，在有界尺度的集中-紧致性约化下，建立了两个非径向散射准则。第一个准则基于固定中心占据窗口和集中中心运动的定量界；第二个准则基于一致低频L²衰减，该衰减产生有限质量、非齐次能量空间中的预紧性、零动量归一化及次线性中心漂移。证明结合了局域Hartree位力恒等式与控制非局部尾项的临界Hardy-Littlewood-Sobolev估计。
英文摘要
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.
