  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.
