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arXiv · 2607.20809

Conditional scattering criteria for cylindrical threshold dynamics of the three-dimensional focusing energy-critical Schr\"odinger equation

Pang-Hung Chung·Dan Han
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Abstract

Below-threshold scattering is studied for the three-dimensional focusing energy-critical Schr\"odinger equation in the cylindrically symmetric class. For soliton-like compact critical elements, two linked rigidity entrances are isolated: a best fixed-axis window condition for the axial center and a low-frequency tail smallness condition. A shifted localized virial estimate and a finite-mass virial argument after axial zero-momentum normalization exclude these entrances, yielding a conditional cylindrical threshold scattering criterion via compactness reduction.

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Pang-Hung Chung, Dan Han. 2026-07-23. Conditional scattering criteria for cylindrical threshold dynamics of the three-dimensional focusing energy-critical Schr\"odinger equation. https://arxiv.org/abs/2607.20809

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