湿大气三维粘性原始方程组时间周期解的存在性
Existence of Time Periodic Solutions for the 3D Viscous Primitive Equations of Large Scale Monist Atmosphere
摘要: 本文考虑的是在气压坐标下的湿大气三维粘性原始方程组的时间周期解的存在性和唯一性问题。主要运用了Galerkin方法，即首先利用Leray-Schauder不动点定理来证明大气原始方程组具有周期性的近似解的存在性，然后再证明这个近似解在其工作空间的收敛性，从而得到大气原始方程组的周期解的存在性，并证明了其唯一性。
Abstract: In this paper, we consider the existence of time periodic solutions of the 3D viscous primitive equations of large-scale monist atmosphere. We used the Galerkin method. Firstly, by Leray-Schauder fixed point theorem, we prove the existence of approximate solutions of the primitive equations, then we show the convergence of the approximate solutions, and we also get the uniqueness to the primitive equations.
文章引用：罗维. 湿大气三维粘性原始方程组时间周期解的存在性[J]. 应用数学进展, 2025, 14(11): 76-89. https://doi.org/10.12677/aam.2025.1411463

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