AI 中文总结
该研究针对$\mathbb R^3$中光滑闭合超曲面领圈邻域内的原始方程，借助极大$L_q$正则性框架与流体静力学亥姆霍兹投影，证明了无初始数据小性假设下强解的整体存在性、唯一性及正则性，且解关于时间和空间联合$C^\text{\infty}$。
AI 中文摘要
本文研究了$\mathbb R^3$中光滑闭合超曲面的领圈邻域内的原始方程。利用极大$L_q$正则性框架与流体静力学亥姆霍兹投影，我们建立了强解的存在性、唯一性及正则性结果。基于这些局部适定性结果，我们推导了合适的先验估计，并证明了在不对初始数据施加任何小性假设的情况下强解的整体存在性。此外，我们还证明了解关于时间和空间是联合$C^\text{\infty}$的。
英文摘要
In this paper, we study the primitive equations in a collar neighborhood of a smooth closed hypersurface in ${\mathbb R}^3$. Using the framework of maximal $L_q$-regularity and the hydrostatic Helmholtz projection, we establish existence, uniqueness, and regularity results for strong solutions. Building on these local well-posedness results, we derive suitable a priori estimates and prove the global existence of strong solutions without imposing any smallness assumptions for the initial data. Moreover, we show that the solutions are $C^\infty$ jointly in time and space.
Comments52 pages
