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

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.

KEYWORDS:

• Stochastic Navier–Stokes–Voigt equations
• existence
• uniqueness
• stationary solution
• mean square exponential stability
• pathwise exponential stability

2010 MATHEMATICS SUBJECT CLASSIFICATIONS:

• 60H15
• 35Q35
• 60H30
• 35B35

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.