The primitive equations with stochastic wind driven boundary conditions
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2020
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| _version_ | 1866915173787238400 |
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| author | Binz, Tim Hieber, Matthias Hussein, Amru Saal, Martin |
| author_facet | Binz, Tim Hieber, Matthias Hussein, Amru Saal, Martin |
| contents | The primitive equations for geophysical flows are studied under the influence of {\em stochastic wind driven boundary conditions} modeled by a cylindrical Wiener process. We adapt an approach by Da Prato and Zabczyk for stochastic boundary value problems to define a notion of solutions. Then a rigorous treatment of these stochastic boundary conditions, which combines stochastic and deterministic methods, yields that these equations admit a unique, local pathwise solution within the anisotropic $L^q_t$-$H^{-1,p}_zL^p_{xy}$-setting. This solution is constructed in critical spaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2009_09449 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | The primitive equations with stochastic wind driven boundary conditions Binz, Tim Hieber, Matthias Hussein, Amru Saal, Martin Probability Analysis of PDEs Primary: 35Q86, Secondary: 35R60, 60H15, 76D03, 76M35, 76U60, 35K61 The primitive equations for geophysical flows are studied under the influence of {\em stochastic wind driven boundary conditions} modeled by a cylindrical Wiener process. We adapt an approach by Da Prato and Zabczyk for stochastic boundary value problems to define a notion of solutions. Then a rigorous treatment of these stochastic boundary conditions, which combines stochastic and deterministic methods, yields that these equations admit a unique, local pathwise solution within the anisotropic $L^q_t$-$H^{-1,p}_zL^p_{xy}$-setting. This solution is constructed in critical spaces. |
| title | The primitive equations with stochastic wind driven boundary conditions |
| topic | Probability Analysis of PDEs Primary: 35Q86, Secondary: 35R60, 60H15, 76D03, 76M35, 76U60, 35K61 |
| url | https://arxiv.org/abs/2009.09449 |