Optimal Gevrey stability of hydrostatic approximation for the Navier-Stokes equations in a thin domain
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| _version_ | 1866912124661399552 |
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| author | Wang, Chao Wang, Yuxi |
| author_facet | Wang, Chao Wang, Yuxi |
| contents | In this paper, we study the hydrostatic approximation for the Navier-Stokes system in a thin domain. When the convex initial data with Gevrey regularity of optimal index 3/2 in x variable and Sobolev regularity in y variable, we justify the limit from the anisotropic Navier-Stokes system to the hydrostatic Navier-Stokes/Prandtl system. Due to our method in the paper is independent of ε, by the same argument, we also get the hydrostatic Navier-Stokes/Prandtl system is well-posedness in the optimal Gevrey space. Our results improve the Gevrey index in [14, 34] whose Gevrey index is 9/8 . |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2206_03873 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Optimal Gevrey stability of hydrostatic approximation for the Navier-Stokes equations in a thin domain Wang, Chao Wang, Yuxi Analysis of PDEs In this paper, we study the hydrostatic approximation for the Navier-Stokes system in a thin domain. When the convex initial data with Gevrey regularity of optimal index 3/2 in x variable and Sobolev regularity in y variable, we justify the limit from the anisotropic Navier-Stokes system to the hydrostatic Navier-Stokes/Prandtl system. Due to our method in the paper is independent of ε, by the same argument, we also get the hydrostatic Navier-Stokes/Prandtl system is well-posedness in the optimal Gevrey space. Our results improve the Gevrey index in [14, 34] whose Gevrey index is 9/8 . |
| title | Optimal Gevrey stability of hydrostatic approximation for the Navier-Stokes equations in a thin domain |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2206.03873 |