带Poisson跳随机Navier-Stokes方程解的指数稳定性分析

摘要

The influence of the P oisson jumps upon the stochastic Navier-Stokes equations has never been consid-ered. This paper discusses the exponential stability of solutions to the stochastic Navier-Stokes equations with Pois-son jumps, on the condition that the system is perturbed by random external environment introducing the definition of solution to the stochastic Navier-Stokes equations and using continuous martingale property, By using Ito^formu-la, Gronwall lemma and extended Gronwall lemma, a sufficient condition of exponential stability is established. This result is an improvement and extension of existing results.%对随机 Navier-Stokes方程的讨论,通常没有考虑P oisson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P oisson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。