Exponential ergodicity for a stochastic two-layer quasi-geostrophic model
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
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2022
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| _version_ | 1866913617216012288 |
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| author | Carigi, Giulia Bröcker, Jochen Kuna, Tobias |
| author_facet | Carigi, Giulia Bröcker, Jochen Kuna, Tobias |
| contents | Ergodic properties of a stochastic medium complexity model for atmosphere and ocean dynamics are analysed. More specifically, a two-layer quasi-geostrophic model for geophysical flows is studied, with the upper layer being perturbed by additive noise. This model is popular in the geosciences, for instance to study the effects of a stochastic wind forcing on the ocean. A rigorous mathematical analysis however meets with the challenge that in the model under study, the noise configuration is spatially degenerate as the stochastic forcing acts only on the top layer. Exponential convergence of solutions laws to the invariant measure is established, implying a spectral gap of the associated Markov semigroup on a space of Hölder continuous functions. The approach provides a general framework for generalised coupling techniques suitable for applications to dissipative SPDEs. In case of the two-layer quasi-geostrophic model, the results require the second layer to obey a certain passivity condition. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2201_09823 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Exponential ergodicity for a stochastic two-layer quasi-geostrophic model Carigi, Giulia Bröcker, Jochen Kuna, Tobias Probability Analysis of PDEs 37L40, 76U60 (Primary) 60H15, 86A08 (Secondary) Ergodic properties of a stochastic medium complexity model for atmosphere and ocean dynamics are analysed. More specifically, a two-layer quasi-geostrophic model for geophysical flows is studied, with the upper layer being perturbed by additive noise. This model is popular in the geosciences, for instance to study the effects of a stochastic wind forcing on the ocean. A rigorous mathematical analysis however meets with the challenge that in the model under study, the noise configuration is spatially degenerate as the stochastic forcing acts only on the top layer. Exponential convergence of solutions laws to the invariant measure is established, implying a spectral gap of the associated Markov semigroup on a space of Hölder continuous functions. The approach provides a general framework for generalised coupling techniques suitable for applications to dissipative SPDEs. In case of the two-layer quasi-geostrophic model, the results require the second layer to obey a certain passivity condition. |
| title | Exponential ergodicity for a stochastic two-layer quasi-geostrophic model |
| topic | Probability Analysis of PDEs 37L40, 76U60 (Primary) 60H15, 86A08 (Secondary) |
| url | https://arxiv.org/abs/2201.09823 |