English

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.

Keywords

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

R2 v1 2026-06-24T10:30:37.291Z