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arXiv · 2605.20715

Threshold dynamics for the 4$d$ mass-energy double critical NLS

Alex H. Ardila·Zuyu Ma·Jason Murphy·Jiqiang Zheng
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Abstract

We consider the 4$d$ mass-energy double critical NLS \[ (i\partial_t+\Delta)u = -|u|^2 u + |u| u. \] In Luo (2024) and Cheng--Miao--Zhao (2016), the authors established a scattering/blowup dichotomy for solutions satisfying the energy constraint $E(u_0)< E^c(W)$, where $W$ is the energy-critical NLS ground state and $E^c$ is the energy for the underlying cubic NLS. We prove that the scattering/blowup dichotomy persists even at the energy threshold $E(u_0)=E^c(W)$.

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Alex H. Ardila, Zuyu Ma, Jason Murphy, Jiqiang Zheng. 2026-05-20. Threshold dynamics for the 4$d$ mass-energy double critical NLS. https://arxiv.org/abs/2605.20715

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