Global well-posedness of the 3D primitive equations with horizontal viscosity and vertical diffusivity II: close to $H^1$ initial data
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arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866910564806033408 |
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| author | Cao, Chongsheng Li, Jinkai Titi, Edriss S. Wang, Dong |
| author_facet | Cao, Chongsheng Li, Jinkai Titi, Edriss S. Wang, Dong |
| contents | In this paper, we consider the initial-boundary value problem to the three-dimensional primitive equations for the oceanic and atmospheric dynamics with only horizontal eddy viscosities in the horizontal momentum equations and only vertical diffusivity in the temperature equation in the domain $Ω=M\times(-h,h)$, with $M=(0,1)\times(0,1)$. Global well-posedness of strong solutions is established, for any initial data $(v_0,T_0) \in H^1(Ω)\cap L^\infty(Ω)$ with $(\partial_z v_0, \nabla_H T_0) \in L^q(Ω)$ and $v_0 \in L_z^1(B^1_{q,2}(M))$, for some $q \in (2,\infty)$, by using delicate energy estimates and maximal regularity estimate in the anisotropic setting. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_06932 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Global well-posedness of the 3D primitive equations with horizontal viscosity and vertical diffusivity II: close to $H^1$ initial data Cao, Chongsheng Li, Jinkai Titi, Edriss S. Wang, Dong Analysis of PDEs Mathematical Physics 26D10, 35Q35, 35Q86, 76D03, 76D05, 86A05, 86A10 In this paper, we consider the initial-boundary value problem to the three-dimensional primitive equations for the oceanic and atmospheric dynamics with only horizontal eddy viscosities in the horizontal momentum equations and only vertical diffusivity in the temperature equation in the domain $Ω=M\times(-h,h)$, with $M=(0,1)\times(0,1)$. Global well-posedness of strong solutions is established, for any initial data $(v_0,T_0) \in H^1(Ω)\cap L^\infty(Ω)$ with $(\partial_z v_0, \nabla_H T_0) \in L^q(Ω)$ and $v_0 \in L_z^1(B^1_{q,2}(M))$, for some $q \in (2,\infty)$, by using delicate energy estimates and maximal regularity estimate in the anisotropic setting. |
| title | Global well-posedness of the 3D primitive equations with horizontal viscosity and vertical diffusivity II: close to $H^1$ initial data |
| topic | Analysis of PDEs Mathematical Physics 26D10, 35Q35, 35Q86, 76D03, 76D05, 86A05, 86A10 |
| url | https://arxiv.org/abs/2408.06932 |