Ergodicity of the 2D Navier-Stokes Equations with Degenerate Multiplicative Noise

• 作 者: Zhao Dong
• 机 构: ChineseAcademyofSciences
• 出 处: 第三届随机动力系统国际会议(Third International Conference on Random Dynam
• 发表日期: 2013年7期

　　Consider the two-dimensional, incompressible Navier-Stokes equations on the torus T2 = [-π,π]2 driven by a degenerate noise dωt = νΔωtdt + B(Κωt,ωt)dt +m∑i=1 qi(ωt)eidBi(t) We prove that the semigroup Pt generated by the solutions to (0.1) has asymptotically strong Feller property. Moreover, we also prove that semigroup {Pt}t≥0 is exponentially ergodic in some sense.