论文标题
Markov Switching的三维随机Navier-Stokes方程的Ergodicity
Ergodicity for Three-Dimensional Stochastic Navier-Stokes Equations with Markov Switching
论文作者
论文摘要
研究了三维随机的Navier-Stokes方程的渐近行为，其中Markov在附加噪声中进行了Markov切换，以在三维空间中有界域中的不可压缩流体流动。为了研究这样的系统，我们介绍了一个正则方程式家族，并首先研究了正则方程的渐近行为。存在正规化系统的奇异措施是通过Krylov-Bogolyubov方法确定的。然后，通过从正规化系统家族的千古量度量中提取限制来获得原始系统的固定度量的存在。
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.
