论文标题
Boussinesq方程的静静力近似，并在薄域中旋转
The hydrostatic approximation of the Boussinesq equations with rotation in a thin domain
论文作者
论文摘要
在本文中，我们稍微改善了全球存在的结果[9]。更确切地说，在h^1 $的初始数据$（v_0，t_0）\ in l^4 $中，只有水平粘度和扩散率仅具有水平粘度和扩散率的原始方程的全球存在。 Moreover, we prove that the scaled Boussinesq equations with rotation strongly converge to the primitive equations with only horizontal viscosity and diffusivity, in the cases of $H^1$ initial data, $H^1$ initial data with additional regularity $\partial_z v_0 \in L^4$ and $H^2$ initial data, respectively, as the aspect ration parameter $λ$ goes to zero, and the rate of收敛是$ O（λ^{η/2}）$的顺序，$η= \ min \ {2，β-2，γ-2，γ-2\}（2 <β，γ<\ infty）$。收敛的结果意味着对静液压近似的严格理由。
In this paper, we improve the global existence result in [9] slightly. More precisely, the global existence of strong solutions to the primitive equations with only horizontal viscosity and diffusivity is obtained under the assumption of initial data $(v_0,T_0) \in H^1$ with $\partial_z v_0 \in L^4$. Moreover, we prove that the scaled Boussinesq equations with rotation strongly converge to the primitive equations with only horizontal viscosity and diffusivity, in the cases of $H^1$ initial data, $H^1$ initial data with additional regularity $\partial_z v_0 \in L^4$ and $H^2$ initial data, respectively, as the aspect ration parameter $λ$ goes to zero, and the rate of convergence is of the order $O(λ^{η/2})$ with $η=\min\{2,β-2,γ-2\}(2<β,γ<\infty)$. The convergence result implies a rigorous justification of the hydrostatic approximation.
