Asymptotic behavior of solutions to the three-dimensional stochastic Leray-α model-Reference-Cited by-同舟云学术

Asymptotic behavior of solutions to the three-dimensional stochastic Leray-α model

Published:2022-05-31 Issue:2 Volume:30 Page:137-148
ISSN:0926-6364
Container-title:Random Operators and Stochastic Equations
language:en
Short-container-title:

Author:

Thanh Nguyen Van¹,Tuan Tran Quoc²

Affiliation:

1. VNU University Of Languages and International Studies , Vietnam National University , Ha Noi, 2 Pham Van Dong, Cau Giay , Hanoi , Vietnam

2. Department of Mathematics , Hanoi National University of Education , 136 Xuan Thuy, Cau Giay , Hanoi , Vietnam

Abstract

Abstract We consider the three-dimensional stochastic Leray-α model with homogeneous Dirichlet boundary conditions and infinite-dimensional Wiener process. We first study the mean square and pathwise exponential stability of a stationary solution to the model. Then we show that one can stabilize an unstable stationary solution by using a multiplicative Itô noise of sufficient intensity or a linear internal feedback control with support large enough.

Publisher

Walter de Gruyter GmbH

Subject

Statistics and Probability,Analysis

Link

https://www.degruyter.com/document/doi/10.1515/rose-2022-2077/pdf

Reference24 articles.

1. H. Ali and P. Kaplický, Existence and regularity of solutions to the Leray-α model with Navier slip boundary conditions, Electron. J. Differential Equations 2016 (2016), Paper No. 235.

2. C. T. Anh and B. H. Bach, Discrete data assimilation algorithm for the three-dimensional Leray-α model, Bull. Pol. Acad. Sci. Math. 66 (2018), no. 2, 143–156.

3. V. Barbu, Note on the internal stabilization of stochastic parabolic equations with linearly multiplicative Gaussian noise, ESAIM Control Optim. Calc. Var. 19 (2013), no. 4, 1055–1063.

4. V. Barbu and C. Lefter, Internal stabilizability of the Navier–Stokes equations, Systems Control Lett. 48 (2003), 161–167.

5. H. Bessaih and P. A. Razafimandimby, On the rate of convergence of the 2-D stochastic Leray-α model to the 2-D stochastic Navier–Stokes equations with multiplicative noise, Appl. Math. Optim. 74 (2016), no. 1, 1–25.

Cited by 1 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. On an optimal control problem of the Leray-α model;Journal of Computational and Applied Mathematics;2024-01