科研之友
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摘要
The stochastic 3D Navier-Stokes equation with damping driven by a multiplicative noise is considered in this paper. The existence of invariant measures is proved for 3 < beta <= 5 with any alpha>0 and alpha >= 1/2 as beta = 3. Using asymptotic strong Feller property, the uniqueness of invariant measures is obtained for the degenerate additive noise. The existence of a random attractor for the random dynamical systems generated by the solution of stochastic 3D Navier-Stokes equations with damping is proved for beta > 3 with any alpha > 0 and alpha >= 1/2 as beta = 3.
