Global well-posedness of the dynamical sine-Gordon model up to $6π$
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866913989641895936 |
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| author | Bringmann, Bjoern Cao, Sky |
| author_facet | Bringmann, Bjoern Cao, Sky |
| contents | We prove the global well-posedness of the dynamical sine-Gordon model up to the third threshold, i.e., for parameters $β^2 < 6π$. The key novelty in our approach is the introduction of the so-called resonant equation, whose solution is entirely deterministic and completely captures the size of the solution to the dynamical sine-Gordon model. The probabilistic fluctuations in the dynamical sine-Gordon model are then controlled using uniform estimates for modified stochastic objects. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_15493 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Global well-posedness of the dynamical sine-Gordon model up to $6π$ Bringmann, Bjoern Cao, Sky Analysis of PDEs Mathematical Physics Probability 60H17 We prove the global well-posedness of the dynamical sine-Gordon model up to the third threshold, i.e., for parameters $β^2 < 6π$. The key novelty in our approach is the introduction of the so-called resonant equation, whose solution is entirely deterministic and completely captures the size of the solution to the dynamical sine-Gordon model. The probabilistic fluctuations in the dynamical sine-Gordon model are then controlled using uniform estimates for modified stochastic objects. |
| title | Global well-posedness of the dynamical sine-Gordon model up to $6π$ |
| topic | Analysis of PDEs Mathematical Physics Probability 60H17 |
| url | https://arxiv.org/abs/2410.15493 |