Existence and non-existence of minimizers for a multi-particle model with concave nonlinearity
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866911139405758464 |
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| author | Gontier, David Lahbabi, Salma Nodari, Simona Rota |
| author_facet | Gontier, David Lahbabi, Salma Nodari, Simona Rota |
| contents | We study a multi--particle model including a kinetic energy and a non linear local self-interaction, both in the bosonic and fermionic cases. In both cases, we prove that the model is well-posed if the number of particles is large enough. In particular, we show that there is a nonlinearity for which the model with $N=2$ particles is well-posed, while the model with $N=1$ is not. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_04952 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Existence and non-existence of minimizers for a multi-particle model with concave nonlinearity Gontier, David Lahbabi, Salma Nodari, Simona Rota Analysis of PDEs Mathematical Physics We study a multi--particle model including a kinetic energy and a non linear local self-interaction, both in the bosonic and fermionic cases. In both cases, we prove that the model is well-posed if the number of particles is large enough. In particular, we show that there is a nonlinearity for which the model with $N=2$ particles is well-posed, while the model with $N=1$ is not. |
| title | Existence and non-existence of minimizers for a multi-particle model with concave nonlinearity |
| topic | Analysis of PDEs Mathematical Physics |
| url | https://arxiv.org/abs/2509.04952 |