2022/03/29 by Po‐Han Hsu, Hsu, Po-Han, P. Sundar +1
Economics, Econometrics and Finance · Engineering · Mathematics · #35Q30 #37L40 #60J75 #FOS: Mathematics #Navier-Stokes equation solutions #Probability (math.PR) #Stability and Controllability of Differential Equations #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.2203.15749
openalex publication_date 2022/03/29 · openalex created_date 2022/04/03 · openalex updated_date 2026/07/28
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.