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arXiv · 2203.15749

Ergodicity for Three-Dimensional Stochastic Navier-Stokes Equations with Markov Switching

Po-Han Hsu·Padmanabhan Sundar
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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.

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Po-Han Hsu, Padmanabhan Sundar. 2022-03-29. Ergodicity for Three-Dimensional Stochastic Navier-Stokes Equations with Markov Switching. https://arxiv.org/abs/2203.15749

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