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

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:385

Article

Taniguchi, Takeshi

关键词: Stochastic Navier-Stokes equations;    Poisson processes;   

DOI  :  10.1016/j.jmaa.2011.06.076

来源: Elsevier

【 摘 要 】

Let D be a bounded or unbounded open domain of 2-dimensional Euclidean space R(2). If the boundary partial derivative D = Gamma exists, then we assume that the boundary is smooth. In this paper assuming that the kinematic viscosity v > 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: {dX(t) = [v Delta X(t) + < X(t), del > X(t) + f(t, X(t)) + F(t, X(t)) -del p]dt + g(t, X(t))dW(t) + integral(u)k(t, X(t), y)q(dt dy), div X = 0 in [0,infinity) x D, where X(t,x) = phi(t, x) is the initial function for x is an element of D and t is an element of [-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 partial derivative D, then X(t,x) = 0 on [0, infinity) x partial derivative D. (C) 2011 Elsevier Inc. All rights reserved.

【 授权许可】

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