Ergodicity for Three-Dimensional Stochastic Navier-Stokes Equations with Markov Switching
Probability
2022-03-30 v1
Abstract
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.
Cite
@article{arxiv.2203.15749,
title = {Ergodicity for Three-Dimensional Stochastic Navier-Stokes Equations with Markov Switching},
author = {Po-Han Hsu and Padmanabhan Sundar},
journal= {arXiv preprint arXiv:2203.15749},
year = {2022}
}
Comments
arXiv admin note: text overlap with arXiv:2203.14442