Well-posedness and long time dynamics for a quasi-geostrophic ocean-atmosphere model with radiation balance
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| Format: | Preprint |
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2025
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| _version_ | 1866914214656868352 |
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| author | Fornasaro, Federico Kuna, Tobias Carigi, Giulia |
| author_facet | Fornasaro, Federico Kuna, Tobias Carigi, Giulia |
| contents | We investigate a coupled atmosphere-ocean model including the mechanical and thermodynamical interaction between the two fluids for the mid-latitudes. The formulation combines a multilayer quasi-geostrophic dynamical framework with temperature equations incorporating long- and short-wave radiative forcing, as in energy balance models. Within a suitable functional framework, we establish the existence and uniqueness of solutions, and their continuous dependence on the radiation parameters. We also prove that the long-time dynamics are described by a finite-dimensional global attractor and, moreover, that the system possesses a finite set of determining modes that governs its asymptotic behaviour. In particular, we show that the long-term evolution of the ocean's temperature can be reconstructed solely from observations of the velocity fields across the model's layers. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2512_19556 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Well-posedness and long time dynamics for a quasi-geostrophic ocean-atmosphere model with radiation balance Fornasaro, Federico Kuna, Tobias Carigi, Giulia Analysis of PDEs Mathematical Physics 35Q86, 35B40, 35B41, 86A08, 76U60 We investigate a coupled atmosphere-ocean model including the mechanical and thermodynamical interaction between the two fluids for the mid-latitudes. The formulation combines a multilayer quasi-geostrophic dynamical framework with temperature equations incorporating long- and short-wave radiative forcing, as in energy balance models. Within a suitable functional framework, we establish the existence and uniqueness of solutions, and their continuous dependence on the radiation parameters. We also prove that the long-time dynamics are described by a finite-dimensional global attractor and, moreover, that the system possesses a finite set of determining modes that governs its asymptotic behaviour. In particular, we show that the long-term evolution of the ocean's temperature can be reconstructed solely from observations of the velocity fields across the model's layers. |
| title | Well-posedness and long time dynamics for a quasi-geostrophic ocean-atmosphere model with radiation balance |
| topic | Analysis of PDEs Mathematical Physics 35Q86, 35B40, 35B41, 86A08, 76U60 |
| url | https://arxiv.org/abs/2512.19556 |