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Stochastics
An International Journal of Probability and Stochastic Processes
Volume 91, 2019 - Issue 4
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Articles

On the existence and long-time behavior of solutions to stochastic three-dimensional Navier–Stokes–Voigt equations

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Pages 485-513 | Received 19 Jun 2017, Accepted 19 Nov 2018, Published online: 26 Nov 2018
 

ABSTRACT

We consider the 3D stochastic Navier–Stokes–Voigt equations in bounded domains with the homogeneous Dirichlet boundary condition and infinite-dimensional Wiener process. First, we prove the existence and uniqueness of solutions to the problem. Then we investigate the mean square exponential stability and the almost sure exponential stability of the stationary solutions.

2010 MATHEMATICS SUBJECT CLASSIFICATIONS:

Acknowledgements

The authors would like to thank the reviewers for the helpful comments and suggestions which improved the presentation of the paper.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by the Vietnam National University, Hanoi, under grant number QG.18.33.

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