具有马尔可夫切换的三维随机Navier-Stokes方程的遍历性

IF 0.8 4区数学 Q3 MATHEMATICS, APPLIED

Stochastic Analysis and Applications Pub Date : 2022-03-28 DOI:10.1080/07362994.2023.2213755

Po-Han Hsu, P. Sundar

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引用次数: 1

摘要

针对三维空间中不可压缩流体在有界域中的流动，研究了加性噪声中具有马尔可夫切换的三维随机Navier-Stokes方程的渐近性。为了研究这样一个系统，我们引入了一组正则化方程，并首先研究了正则化方程的渐近性质。利用Krylov-Bogolyubov方法建立了正则化系统遍历测度的存在性。然后通过从正则化系统族的遍历测度中提取一个极限，得到了原系统的平稳测度的存在性。

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Ergodicity for three-dimensional stochastic Navier–Stokes equations with Markovian switching

Asymptotic behavior of the three-dimensional stochastic Navier-Stokes equations with Markov switching in additive noises is studied for incompressible fluid flow in a bounded domain in the three-dimensional space. To study such a system, we introduce a family of regularized equations and investigate the asymptotic behavior of the regularized equations first. The existence an ergodic measure for the regularized system is established via the Krylov-Bogolyubov method. Then the existence of an stationary measure to the original system is obtained by extracting a limit from the ergodic measures of the family of the regularized system.

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来源期刊

Stochastic Analysis and Applications 数学-统计学与概率论

CiteScore

2.70

自引率

7.70%

发文量

审稿时长

6-12 weeks

期刊介绍： Stochastic Analysis and Applications presents the latest innovations in the field of stochastic theory and its practical applications, as well as the full range of related approaches to analyzing systems under random excitation. In addition, it is the only publication that offers the broad, detailed coverage necessary for the interfield and intrafield fertilization of new concepts and ideas, providing the scientific community with a unique and highly useful service.