Ground States of Attractive Fermi Schrödinger Systems with Ring-Shaped Potentials
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866915839139119104 |
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| author | Guo, Yujin Li, Yan Wu, Shuang |
| author_facet | Guo, Yujin Li, Yan Wu, Shuang |
| contents | As an application of the finite-rank Lieb-Thirring inequality established in [R. L. Frank, D. Gontier and M. Lewin, Comm. Math. Phys., 2021], we study ground states of mass-critical N-coupled Fermi nonlinear Schrödinger systems with attractive interactions in $\mathbb{R}^3$, which are trapped in ring-shaped potentials. For any given $N\in\mathbb{N}^+$, we prove that ground states exist if $0<a<a_N^*$, where $a$ denotes the strength of attractive interactions in the system, and $a_N^*$ is the best constant of a finite-rank Lieb-Thirring inequality. Moreover, for some $N\in\mathbb{N}^+$, we also prove the nonexistence of minimizers for the system as soon as $a\geq a_N^*$. Applying the energy estimates and the blow-up analysis, we further analyze the mass concentration behavior of ground states for the system as $a\nearrow a_N^*$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_05903 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Ground States of Attractive Fermi Schrödinger Systems with Ring-Shaped Potentials Guo, Yujin Li, Yan Wu, Shuang Analysis of PDEs As an application of the finite-rank Lieb-Thirring inequality established in [R. L. Frank, D. Gontier and M. Lewin, Comm. Math. Phys., 2021], we study ground states of mass-critical N-coupled Fermi nonlinear Schrödinger systems with attractive interactions in $\mathbb{R}^3$, which are trapped in ring-shaped potentials. For any given $N\in\mathbb{N}^+$, we prove that ground states exist if $0<a<a_N^*$, where $a$ denotes the strength of attractive interactions in the system, and $a_N^*$ is the best constant of a finite-rank Lieb-Thirring inequality. Moreover, for some $N\in\mathbb{N}^+$, we also prove the nonexistence of minimizers for the system as soon as $a\geq a_N^*$. Applying the energy estimates and the blow-up analysis, we further analyze the mass concentration behavior of ground states for the system as $a\nearrow a_N^*$. |
| title | Ground States of Attractive Fermi Schrödinger Systems with Ring-Shaped Potentials |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2603.05903 |