Invariant Gibbs dynamics for the hyperbolic sinh-Gordon model
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866915800396333056 |
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| author | Forlano, Justin Zine, Younes |
| author_facet | Forlano, Justin Zine, Younes |
| contents | We study the hyperbolic defocusing sinh-Gordon model with parameter $β^2>0$ and its associated Gibbs dynamics on the two-dimensional torus. We establish global well-posedness of the model for a certain range of parameters $β^2>0$ with the corresponding Gibbs measure initial data and prove invariance of the Gibbs measure under the flow, thereby resolving a question posed by Oh, Robert, and Wang (2019). Our physical space approach hinges on developing a novel $L^\infty$-based well-posedness theory for wave equations with exponential-type nonlinearities, going beyond the classical $L^2$-based framework. This refinement allows us to fully leverage structural properties of Gaussian multiplicative chaos. As a by-product of our method, we also obtain an improved well-posedness theory for the hyperbolic Liouville model. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_14996 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Invariant Gibbs dynamics for the hyperbolic sinh-Gordon model Forlano, Justin Zine, Younes Analysis of PDEs Mathematical Physics Probability 35L71 (Primary) 60H15, 81T08 (Secondary) We study the hyperbolic defocusing sinh-Gordon model with parameter $β^2>0$ and its associated Gibbs dynamics on the two-dimensional torus. We establish global well-posedness of the model for a certain range of parameters $β^2>0$ with the corresponding Gibbs measure initial data and prove invariance of the Gibbs measure under the flow, thereby resolving a question posed by Oh, Robert, and Wang (2019). Our physical space approach hinges on developing a novel $L^\infty$-based well-posedness theory for wave equations with exponential-type nonlinearities, going beyond the classical $L^2$-based framework. This refinement allows us to fully leverage structural properties of Gaussian multiplicative chaos. As a by-product of our method, we also obtain an improved well-posedness theory for the hyperbolic Liouville model. |
| title | Invariant Gibbs dynamics for the hyperbolic sinh-Gordon model |
| topic | Analysis of PDEs Mathematical Physics Probability 35L71 (Primary) 60H15, 81T08 (Secondary) |
| url | https://arxiv.org/abs/2602.14996 |