Existence and order of the self--binding transition in non--local non--linear Schrödinger equations
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866908515946201088 |
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| author | Ikoma, Norihisa Myśliwy, Krzysztof |
| author_facet | Ikoma, Norihisa Myśliwy, Krzysztof |
| contents | We consider a class of non--linear and non--local functionals giving rise to the Choquard equation with a suitably regular interaction potential, modelling, i.e., gases with impurities and axion stars. We study how existence of minimizers depends on the coupling constant, and find that there is a critical interaction strength needed for the minimizers to exist, both in dimensions two and three. In $d=3$, a minimizer exists also at the critical coupling but none do in $d=2$ under suitable assumptions on the potential. We also establish that in $d=3$ there exist other critical points beyond the global minimizer. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_06988 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Existence and order of the self--binding transition in non--local non--linear Schrödinger equations Ikoma, Norihisa Myśliwy, Krzysztof Analysis of PDEs 35A15, 81V70 We consider a class of non--linear and non--local functionals giving rise to the Choquard equation with a suitably regular interaction potential, modelling, i.e., gases with impurities and axion stars. We study how existence of minimizers depends on the coupling constant, and find that there is a critical interaction strength needed for the minimizers to exist, both in dimensions two and three. In $d=3$, a minimizer exists also at the critical coupling but none do in $d=2$ under suitable assumptions on the potential. We also establish that in $d=3$ there exist other critical points beyond the global minimizer. |
| title | Existence and order of the self--binding transition in non--local non--linear Schrödinger equations |
| topic | Analysis of PDEs 35A15, 81V70 |
| url | https://arxiv.org/abs/2504.06988 |