Global well-posedness of the stochastic Abelian-Higgs equations in two dimensions
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2024
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866913369733201920 |
|---|---|
| author | Bringmann, Bjoern Cao, Sky |
| author_facet | Bringmann, Bjoern Cao, Sky |
| contents | We prove the global well-posedness of the stochastic Abelian-Higgs equations in two dimensions. The proof is based on a new covariant approach, which consists of two parts: First, we introduce covariant stochastic objects. The covariant stochastic objects and their multi-linear interactions are controlled using covariant heat kernel estimates. Second, we control nonlinear remainders using a covariant monotonicity formula, which is inspired by earlier work of Hamilton. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_16878 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Global well-posedness of the stochastic Abelian-Higgs equations in two dimensions Bringmann, Bjoern Cao, Sky Analysis of PDEs Mathematical Physics Probability 35R60, 60H17 We prove the global well-posedness of the stochastic Abelian-Higgs equations in two dimensions. The proof is based on a new covariant approach, which consists of two parts: First, we introduce covariant stochastic objects. The covariant stochastic objects and their multi-linear interactions are controlled using covariant heat kernel estimates. Second, we control nonlinear remainders using a covariant monotonicity formula, which is inspired by earlier work of Hamilton. |
| title | Global well-posedness of the stochastic Abelian-Higgs equations in two dimensions |
| topic | Analysis of PDEs Mathematical Physics Probability 35R60, 60H17 |
| url | https://arxiv.org/abs/2403.16878 |