三维热带气候模型轨道统计解的存在性、退化正则性与极限行为  

Existence,Degenerate Regularity and Limit Behavior of Trajectory Statistical Solution for the 3D Tropical Climate Model

作　　者：杨虎军 韩晓玲 赵才地[2] Hujun Yang;Xiaoling Han;Caidi Zhao(School of Mathematics and Statistics,Northwest Normal University,Lanzhou 730070,P.R.China;College of Mathematics and Physics,Wenzhou University,Wenzhou 325035,P.R.China)

机构地区：[1]西北师范大学数学与统计学院,兰州730070 [2]温州大学数理学院,温州325035

出　　处：《数学学报(中文版)》2025年第2期325-349,共25页Acta Mathematica Sinica:Chinese Series

基　　金：国家自然科学基金面上项目(12371245,11971356),国家自然科学基金地区基金项目(12161079);浙江省自然科学基金重点项目(LZ24A010005)。

摘　　要：本文研究三维热带气候模型的轨道统计解及其性质.作者首先证明带阻尼项的三维热带气候模型存在轨道吸引子,并应用该轨道吸引子和广义Banach极限构造出轨道统计解.然后证明当模型的广义Grashof数足够小时轨道统计解具有退化正则性.最后证明当阻尼系数趋于零时轨道统计解收敛到无阻尼项的三维热带气候模型的轨道统计解.This article studies the trajectory statistical solution and its properties of the 3D tropical climate model.Firstly,the authors establish that the 3D tropical climate model with damping terms possesses a trajectory attractor,and use this trajectory attractor and generalized Banach limit to construct the trajectory statistical solution.Then they prove that the trajectory statistical solution has degenerate regularity provided that the associated generalized Grashof number is small enough.Finally they verify that the trajectory statistical solution converges to that of the 3D tropical climate model without damping term when the damping coefficients tends to zero.

关 键 词：热带气候模型 轨道吸引子 轨道统计解 退化正则性 

分 类 号：O175.8[理学—数学]