环面上不可压缩Oldroyd-B模型的全局指数衰减和无黏极限  

Globally Exponential Decay and Inviscid Limit of the Incompressible Oldroyd-B Model on Torus

作　　者：陈玉莹 潘星宏 Yuying Chen;Xinghong Pan(School of Mathematics and Key Laboratory of MIIT,Nanjing University of Aeronautics and Astronautics,Nanjing 211106,P.R.China)

机构地区：[1]南京航空航天大学数学学院与工信部重点实验室,南京211106

出　　处：《数学学报(中文版)》2025年第1期30-44,共15页Acta Mathematica Sinica:Chinese Series

基　　金：国家自然科学基金资助项目(11801268,12031006,12471222);中央高校基本科研业务费(NS2023039)。

摘　　要：本文首先证明了环面上三维不可压缩Oldroyd-B模型小初值解析解的全局存在性和指数衰减.我们能够得到一个无黏性的先验估计.基于这个先验估计,OldroydB系统的无黏性极限能够被得到.这里我们指出,此系统的非线性二次项的导数比线性部分的高一阶,而我们没有好的结构去克服这种导数损失问题,因此我们只能在解析能量泛函空间中建立全局时间的结果,而不是在有限阶导数的Sobolev空间中得到全局存在性.In this paper,we first prove the global existence and exponential decay of small-data analytical solutions to the three-dimensional incompressible Oldroyd-B model in torus.An a priori estimate of viscosity independence will be obtained.Based on such a priori estimate,we then show validity of the inviscid limit of the Oldroyd-B system.The nonlinear quadratic terms have one more order derivative than the linear part and no good structure is found to overcome this derivative loss problem.So we can only build the global-in-time result in the analytical energy functional space rather than the Sobolev space with finite order derivatives.

关 键 词：全局解析解 无黏性极限 OLDROYD-B 导数损失 

分 类 号：O177.2[理学—数学]