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arXiv · 2508.02608

Dynamics of subcritical threshold solutions for the 4d energy-critical NLS

Zuyu Ma·Changxing Miao·Jason Murphy·Jiqiang Zheng
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Abstract

We study dynamics of the 4$d$ 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.

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Zuyu Ma, Changxing Miao, Jason Murphy, Jiqiang Zheng. 2025-08-04. Dynamics of subcritical threshold solutions for the 4d energy-critical NLS. https://arxiv.org/abs/2508.02608

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