Scattering and Low-Speed Critical Elements for the 3D Focusing Energy-Critical NLS

Pang-Hung Chung; Dan Han

Scattering and Low-Speed Critical Elements for the 3D Focusing Energy-Critical NLS

Analysis of PDEs 2026-07-05 v1 Dynamical Systems

Authors: Pang-Hung Chung , Dan Han

Abstract

The below-threshold scattering problem is considered for the three-dimensional focusing energy-critical nonlinear Schr\"odinger 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.

Keywords

energy-critical NLS scattering virial estimate soliton nonlinear Schrödinger equation

Cite

@article{arxiv.2607.04214,
  title  = {Scattering and Low-Speed Critical Elements for the 3D Focusing Energy-Critical NLS},
  author = {Pang-Hung Chung and Dan Han},
  journal= {arXiv preprint arXiv:2607.04214},
  year   = {2026}
}