Dynamics of subcritical threshold solutions for the 4d energy-critical NLS
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866912518958481408 |
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| author | Ma, Zuyu Miao, Changxing Murphy, Jason Zheng, Jiqiang |
| author_facet | Ma, Zuyu Miao, Changxing Murphy, Jason Zheng, Jiqiang |
| contents | We study dynamics of the 4$d$ energy-critical nonlinear Schrödinger 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_02608 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Dynamics of subcritical threshold solutions for the 4d energy-critical NLS Ma, Zuyu Miao, Changxing Murphy, Jason Zheng, Jiqiang Analysis of PDEs We study dynamics of the 4$d$ energy-critical nonlinear Schrödinger 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. |
| title | Dynamics of subcritical threshold solutions for the 4d energy-critical NLS |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2508.02608 |