带Poisson跳随机Navier-Stokes方程解的指数稳定性分析

An Analysis about the Exponential Stability of Solutions to the Stochastic Navier- Stokes Equations with Poisson Jump

对随机Navier-Stokes方程的讨论,通常没有考虑Poisson跳对系统影响.在假设随机的外界环境对系统产生影响的条件下,给出了带Poisson跳的随机Navier-Stokes方程,利用连续鞅的性质,通过公式,Gronwall引理及广义的Gronwall扩展引理讨论了其解的指数稳定性,并给出了指数稳定性的充分条件。

The influence of the Poisson jumps upon the stochastic Navier - Stokes equations has never been consid ered. This paper discusses the Poisson jumps, on the condition tion of solution to the stochastic formula, GronwaU lished. This result exponential stability of solutions to the stochastic Navier - Stokes equations with that the system is perturbed by random external environment introducing the defini Navier Stokes equations and using continuous martingale property, By using ho^ lemma and extended Gronwall lemma, a sufficient condition of exponential stability is estab- is an improvement and extension of existing results.