Averaging principle for the stochastic primitive equations in the large rotation limit
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866909520797630464 |
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| author | Lin, Quyuan Liu, Rongchang Martinez, Vincent R. |
| author_facet | Lin, Quyuan Liu, Rongchang Martinez, Vincent R. |
| contents | It is known that the unique ergodicity of the viscous primitive equations with additive white-in-time noise remains an open problem. In this work, we demonstrate that, as the rotational intensity approaches infinity, the distribution of any given strong solution, rescaled by the rotation, is attracted to the unique invariant measure of the stochastic limit resonant system. This suggests that the system exhibits nearly unique ergodicity in the large rotation limit. The proof is based on a stochastic averaging principle combined with a coupling argument. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_00991 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Averaging principle for the stochastic primitive equations in the large rotation limit Lin, Quyuan Liu, Rongchang Martinez, Vincent R. Probability Analysis of PDEs 35Q86, 35R60, 37L40, 76D06 It is known that the unique ergodicity of the viscous primitive equations with additive white-in-time noise remains an open problem. In this work, we demonstrate that, as the rotational intensity approaches infinity, the distribution of any given strong solution, rescaled by the rotation, is attracted to the unique invariant measure of the stochastic limit resonant system. This suggests that the system exhibits nearly unique ergodicity in the large rotation limit. The proof is based on a stochastic averaging principle combined with a coupling argument. |
| title | Averaging principle for the stochastic primitive equations in the large rotation limit |
| topic | Probability Analysis of PDEs 35Q86, 35R60, 37L40, 76D06 |
| url | https://arxiv.org/abs/2503.00991 |