Threshold dynamics for the 4$d$ mass-energy double critical NLS
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866916030875435008 |
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| author | Ardila, Alex H. Ma, Zuyu Murphy, Jason Zheng, Jiqiang |
| author_facet | Ardila, Alex H. Ma, Zuyu Murphy, Jason Zheng, Jiqiang |
| contents | We consider the 4$d$ mass-energy double critical NLS \[ (i\partial_t+Δ)u = -|u|^2 u + |u| u. \] 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 $E(u_0)=E^c(W)$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2605_20715 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Threshold dynamics for the 4$d$ mass-energy double critical NLS Ardila, Alex H. Ma, Zuyu Murphy, Jason Zheng, Jiqiang Analysis of PDEs We consider the 4$d$ mass-energy double critical NLS \[ (i\partial_t+Δ)u = -|u|^2 u + |u| u. \] 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 $E(u_0)=E^c(W)$. |
| title | Threshold dynamics for the 4$d$ mass-energy double critical NLS |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2605.20715 |