AI 中文总结
考虑三维聚焦能量临界非线性薛定谔方程的阈值以下散射问题，通过研究类孤子临界元素浓度中心漂移，给出紧致临界解在特定条件下必消失及相应条件散射准则。
AI 中文摘要
考虑三维聚焦能量临界非线性薛定谔方程的阈值以下散射问题。一个主要的非径向障碍是类孤子临界元素浓度中心可能的漂移，这阻止了固定中心局部位力估计直接闭合。结果表明，如果这样一个紧致临界解具有\(L_t^\infty L_x^q\)界且其中心漂移足够慢，则它必定消失。该结果涵盖纯能量、端点\(L^4\)和有限质量情形，并给出了相应的条件散射准则。
英文摘要
The below-threshold scattering problem is considered for the three-dimensional focusing energy-critical nonlinear Schrödinger equation. A main non-radial obstruction is the possible drift of the concentration center of a soliton-like critical element, which prevents a fixed-center localized virial estimate from closing directly. It is shown that such a compact critical solution must vanish if it has an $L_t^\infty L_x^q$ bound and its center drifts sufficiently slowly. The result covers the pure-energy, endpoint $L^4$, and finite-mass regimes and gives a corresponding conditional scattering criterion.
