二维Stokes近似方程组大扰动解的衰减估计  

The decay estimate of large perturbation solutions to two-dimensional Stokes approximate equations

作　　者：王利娟 王维克 王宇澄[2] Lijuan Wang;Weike Wang;Yucheng Wang

机构地区：[1]上海对外经贸大学统计与信息学院,上海201620 [2]上海交通大学数学科学学院,上海200240 [3]上海交通大学自然科学研究院,上海200240 [4]上海交通大学上海市现代分析前沿科学研究基地,上海200240

出　　处：《中国科学：数学》2023年第6期815-838,共24页Scientia Sinica：Mathematica

基　　金：国家自然科学基金(批准号:12271357和11831011);上海市科技创新行动计划(批准号:21JC1403600)资助项目

摘　　要：本文结合频谱域划分的方法和能量估计,充分利用方程中的耗散机制,得到二维Stokes近似方程组Cauchy问题大扰动解的一致估计;并在此基础上应用频谱域的划分方法得到解在某个长时间处的小性结合精细的Green函数的方法,本文得到在时间充分大时解的衰减率的估计.本文试图探索在大扰动情形下利用精细的Green函数技术得到解的衰减估计的一般办法.In this paper,combining the method of spectrum division and energy estimation,and making full use of the dissipation mechanism in the system,we obtain the uniform estimation of the large perturbation solution to the Cauchy problem of the two-dimensional Stokes approximate equation by this method,and define the division method of spectrum domains to obtain the smallness of the solution at a large time.Combining the fine Green's function method,we obtain the estimation of the decay rate of the solution when the time is sufficiently large.We attempt to explore a general method to obtain the best decay estimation of the solution by using the fine Green's function technique in the case of a large disturbance.

关 键 词：一致估计 GREEN函数 耗散机制 频谱分解 

分 类 号：O175[理学—数学]