The stochastic primitive equations with non-isothermal turbulent pressure
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2022
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| _version_ | 1866913569160822784 |
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| author | Agresti, Antonio Hieber, Matthias Hussein, Amru Saal, Martin |
| author_facet | Agresti, Antonio Hieber, Matthias Hussein, Amru Saal, Martin |
| contents | In this paper, we introduce and study the primitive equations with $\textit{non}$-isothermal turbulent pressure and transport noise. They are derived from the Navier-Stokes equations by employing stochastic versions of the Boussinesq and the hydrostatic approximations. The temperature dependence of the turbulent pressure can be seen as a consequence of an additive noise acting on the small vertical dynamics. For such a model we prove global well-posedness in $H^1$ where the noise is considered in both the Itô and Stratonovich formulations. Compared to previous variants of the primitive equations, the one considered here presents a more intricate coupling between the velocity field and the temperature. The corresponding analysis is seriously more involved than in the deterministic setting. Finally, the continuous dependence on the initial data and the energy estimates proven here are new, even in the case of isothermal turbulent pressure. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2210_05973 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | The stochastic primitive equations with non-isothermal turbulent pressure Agresti, Antonio Hieber, Matthias Hussein, Amru Saal, Martin Analysis of PDEs Mathematical Physics Probability Primary 35Q86, Secondary 35R60, 60H15, 76M35, 76U60 In this paper, we introduce and study the primitive equations with $\textit{non}$-isothermal turbulent pressure and transport noise. They are derived from the Navier-Stokes equations by employing stochastic versions of the Boussinesq and the hydrostatic approximations. The temperature dependence of the turbulent pressure can be seen as a consequence of an additive noise acting on the small vertical dynamics. For such a model we prove global well-posedness in $H^1$ where the noise is considered in both the Itô and Stratonovich formulations. Compared to previous variants of the primitive equations, the one considered here presents a more intricate coupling between the velocity field and the temperature. The corresponding analysis is seriously more involved than in the deterministic setting. Finally, the continuous dependence on the initial data and the energy estimates proven here are new, even in the case of isothermal turbulent pressure. |
| title | The stochastic primitive equations with non-isothermal turbulent pressure |
| topic | Analysis of PDEs Mathematical Physics Probability Primary 35Q86, Secondary 35R60, 60H15, 76M35, 76U60 |
| url | https://arxiv.org/abs/2210.05973 |