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Lipschitz区域上一类非自治时滞抛物方程的吸引子
  • 期刊名称：应用数学学报
  • 时间：0
  • 页码：1049-1060
  • 分类：O211.6[理学—概率论与数理统计;理学—数学] TP393[自动化与计算机技术—计算机应用技术;自动化与计算机技术—计算机科学与技术]
  • 作者机构：[1]Department of Mathematics and System Science, National University of Defense Technology, Changsha 410073, P. R. China
  • 相关基金：Project supported by the National Natural Science Foundation of China （No. 10971225）, the Natural Science Foundation of Hunan Province （No. 11JJ3004）, and the Scientific Research Foundation for the Returned Overseas Chinese Scholars, Ministry of Education of China （No. 2009-1001）
  • 相关项目：Levy过程驱动的无穷维随机动力系统的动力学研究
作者： 王圆|黄建华|
关键词： HURST参数, 分数布朗运动, 非牛顿流体, 流体驱动, 流体动力学, 随机, DIRICHLET边界条件, 不可压缩, infinite-dimensional fractional Brownian motion （FBM）, stochastic convolution, stochastic nomNewtonian fluid, random attractor
中文摘要：

A two-dimensional (2D) stochastic incompressible non-Newtonian fluid driven by the genuine cylindrical fractional Brownian motion (FBM) is studied with the Hurst parameter H ∈(1/4,1/2) under the Dirichlet boundary condition. The existence and regularity of the stochastic convolution corresponding to the stochastic non-Newtonian fluids are obtained by the estimate on the spectrum of the spatial differential operator and the identity of the infinite double series in the analytic number theory. The existence of the mild solution and the random attractor of a random dynamical system are then obtained for the stochastic non-Newtonian systems with H ∈(1/2,1) without any additional restriction on the parameter H.

英文摘要：

A two-dimensional （2D） stochastic incompressible non-Newtonian fluid driven by the genuine cylindrical fractional Brownian motion （FBM） is studied with the Hurst parameter ∈ （1/4,1/2） under the Dirichlet boundary condition. The existence and regularity of the stochastic convolution corresponding to the stochastic non-Newtonian fluids are obtained by the estimate on the and the identity of the infinite double series spectrum of the spatial differential operator in the analytic number theory. The existence of the mild solution and the random attractor of a random dynamical system are then obtained for the stochastic non-Newtonian systems with ∈ （1/2,1） without any additional restriction on the parameter H.

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Levy过程驱动的无穷维随机动力系统的动力学研究
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