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Threshold Scattering for the Three-Dimensional Focusing Energy-Critical Nonlinear Schrödinger Equation
Abstract
Threshold scattering below the ground-state energy and gradient is established for the three-dimensional focusing energy-critical nonlinear Schrödinger equation. A single solution-dependent Gaussian interaction scale, mass-free angular coercivity, and a frequency-gap source estimate control the projected dynamics. These estimates yield quartic spacetime integrability and a zero-mass contradiction, without radial symmetry or an a priori L2 bound.
Related
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BibTeX
@misc{chung2026threshold,
title = {{Threshold Scattering for the Three-Dimensional Focusing Energy-Critical Nonlinear Schrödinger Equation}},
author = {Pang-hung Chung and Dan Han},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.10658},
eprint = {2610.10658},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.10658},
}
RIS
TY - UNPB
TI - Threshold Scattering for the Three-Dimensional Focusing Energy-Critical Nonlinear Schrödinger Equation
AU - Pang-hung Chung
AU - Dan Han
PY - 2026
DA - 2026/10/07
PB - arXiv
DO - 10.48550/arxiv.2610.10658
UR - https://arxiv.org/abs/2610.10658
AB - Threshold scattering below the ground-state energy and gradient is established for the three-dimensional focusing energy-critical nonlinear Schrödinger equation. A single solution-dependent Gaussian interaction scale, mass-free angular coercivity, and a frequency-gap source estimate control the projected dynamics. These estimates yield quartic spacetime integrability and a zero-mass contradiction, without radial symmetry or an a priori L^2 bound.
ER -