Singularity formation for the higher dimensional Skyrme model
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866913483188076544 |
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| author | McNulty, Michael |
| author_facet | McNulty, Michael |
| contents | This paper demonstrates that singularities form in the classical $(5+1)$-dimensional, co-rotational Skyrme model. It was recently proven by Chen, Schörkhuber, and the author that the strong field limit of the $(5+1)$-dimensional, co-rotational Skyrme model admits an explicit self-similar solution which is asymptotically stable within backwards light cones. Seeded by the limiting model, we construct an open set of initial data whose evolution within a backwards light cone, according to the full model, suffers a gradient blowup in finite time. Moreover, the singularity develops at the self-similar rate and possesses an asymptotic profile given by the self-similar profile of the strong field model. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_15345 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Singularity formation for the higher dimensional Skyrme model McNulty, Michael Analysis of PDEs Mathematical Physics This paper demonstrates that singularities form in the classical $(5+1)$-dimensional, co-rotational Skyrme model. It was recently proven by Chen, Schörkhuber, and the author that the strong field limit of the $(5+1)$-dimensional, co-rotational Skyrme model admits an explicit self-similar solution which is asymptotically stable within backwards light cones. Seeded by the limiting model, we construct an open set of initial data whose evolution within a backwards light cone, according to the full model, suffers a gradient blowup in finite time. Moreover, the singularity develops at the self-similar rate and possesses an asymptotic profile given by the self-similar profile of the strong field model. |
| title | Singularity formation for the higher dimensional Skyrme model |
| topic | Analysis of PDEs Mathematical Physics |
| url | https://arxiv.org/abs/2408.15345 |