Dynamics of subcritical threshold solutions for the 4d energy-critical NLS
Analysis of PDEs
2025-08-05 v1
Abstract
We study dynamics of the 4 energy-critical nonlinear Schr\"odinger equation at the ground state energy. Previously, Duyckaerts and Merle [Geom. Funct. Anal. (2009)] proved that any radial solution with kinetic energy less than that of the ground state either scatters in both time directions or coincides (modulo symmetries) with a heteroclinic orbit, which scatters in one time direction and converges to the ground state in the other. We extend this result to the non-radial setting.
Keywords
Cite
@article{arxiv.2508.02608,
title = {Dynamics of subcritical threshold solutions for the 4d energy-critical NLS},
author = {Zuyu Ma and Changxing Miao and Jason Murphy and Jiqiang Zheng},
journal= {arXiv preprint arXiv:2508.02608},
year = {2025}
}
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35 pages