Global well-posedness of the 3D primitive equations with horizontal viscosity and vertical diffusivity II: close to $H^1$ initial data
| Autor: | Cao, Chongsheng, Li, Jinkai, Titi, Edriss S., Wang, Dong |
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| Rok vydání: | 2024 |
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| Druh dokumentu: | Working Paper |
| Popis: | 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 $\Omega=M\times(-h,h)$, with $M=(0,1)\times(0,1)$. Global well-posedness of strong solutions is established, for any initial data $(v_0,T_0) \in H^1(\Omega)\cap L^\infty(\Omega)$ with $(\partial_z v_0, \nabla_H T_0) \in L^q(\Omega)$ 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. Comment: arXiv admin note: text overlap with arXiv:1703.02512 |
| Databáze: | arXiv |
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