ASYMPTOTIC BEHAVIOR OF STOCHASTIC ANISOTROPIC NAVIER-STOKES MODELS

doi:10.1007/s10473-025-0524-9

数学物理学报(英文版) ›› 2025, Vol. 45 ›› Issue (5): 2264-2278.doi: 10.1007/s10473-025-0524-9

ASYMPTOTIC BEHAVIOR OF STOCHASTIC ANISOTROPIC NAVIER-STOKES MODELS

Min ZHU¹, Hongshuai DAI^2,*

1. College of Science, Hunan University of Technology, Zhuzhou 412007, China;
2. School of Statistics and Mathematics, Shandong University of Finance and Economics, Jinan 250014, China

收稿日期:2023-12-20 修回日期:2024-12-20 出版日期:2025-09-25 发布日期:2025-10-14

ASYMPTOTIC BEHAVIOR OF STOCHASTIC ANISOTROPIC NAVIER-STOKES MODELS

Min ZHU¹, Hongshuai DAI^2,*

1. College of Science, Hunan University of Technology, Zhuzhou 412007, China;
2. School of Statistics and Mathematics, Shandong University of Finance and Economics, Jinan 250014, China

Received:2023-12-20 Revised:2024-12-20 Online:2025-09-25 Published:2025-10-14
Contact: ^*Hongshuai Dai, E-mail: mathdsh@gmail.com
About author:Min Zhu, E-mail: zhumin0107@hut.edu.cn
Supported by:
Zhu's research was supported by the Natural Science Foundation of Hunan Province of China (2024JJ5123). Dai's research was supported by the Shandong Provincial Natural Science Foundation (ZR2023MA072, ZR2020MA036).

摘要/Abstract

摘要： The existence and uniqueness of stationary solutions to anisotropic Navier-Stokes equations is investigated by a Galerkin technique in this work. Based on this conclusion, we further explore the exponential stability of weak solutions to stochastic anisotropic Navier-Stokes equations. We present a relationship among different growth exponents, which is sufficient to guarantee the existence, uniqueness and exponential stability of stationary solutions.

关键词: asymptotic behavior, stochastic anisotropic Navier-Stokes equation, embedding theorems, anisotropic Sobolev space, stability

Abstract: The existence and uniqueness of stationary solutions to anisotropic Navier-Stokes equations is investigated by a Galerkin technique in this work. Based on this conclusion, we further explore the exponential stability of weak solutions to stochastic anisotropic Navier-Stokes equations. We present a relationship among different growth exponents, which is sufficient to guarantee the existence, uniqueness and exponential stability of stationary solutions.

Key words: asymptotic behavior, stochastic anisotropic Navier-Stokes equation, embedding theorems, anisotropic Sobolev space, stability

中图分类号:

60H15

Min ZHU, Hongshuai DAI. ASYMPTOTIC BEHAVIOR OF STOCHASTIC ANISOTROPIC NAVIER-STOKES MODELS[J]. 数学物理学报(英文版), 2025, 45(5): 2264-2278.

Min ZHU, Hongshuai DAI. ASYMPTOTIC BEHAVIOR OF STOCHASTIC ANISOTROPIC NAVIER-STOKES MODELS[J]. Acta mathematica scientia,Series B, 2025, 45(5): 2264-2278.

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ASYMPTOTIC BEHAVIOR OF STOCHASTIC ANISOTROPIC NAVIER-STOKES MODELS

ASYMPTOTIC BEHAVIOR OF STOCHASTIC ANISOTROPIC NAVIER-STOKES MODELS

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