The existence and asymptotic behaviour of energy solutions to stochastic 2D functional Navier-Stokes equations driven by Levy processes

摘要

Let D be a bounded or unbounded open domain of 2-dimensional Euclidean space R2. If the boundary ?D=Γ exists, then we assume that the boundary is smooth. In this paper assuming that the kinematic viscosity ν>0 is large enough, we discuss the existence and exponential stability of energy solutions to the following 2-dimensional stochastic functional Navier-Stokes equation perturbed by the Levy process:. where X(t,x)=φ(t,x) is the initial function for x∈D and t∈[-r,0] with r>0. It is assumed that f,g,F and k satisfy the Lipschitz condition and the linear growth condition. If there exists the boundary ?. D, then X(t,x)=0 on [0,∞)×?D.