Dynamics of stochastic non-Newtonian fluids driven by fractional Brownian motion with Hurst parameter $$H \in \left( {\tfrac{1} {4},\tfrac{1} {2}} \right)$$
Dynamics of stochastic non-Newtonian fluids driven by fractional Brownian motion with Hurst parameter $$H \in \left( {\tfrac{1} {4},\tfrac{1} {2}} \right)$$
复制标题
DOI：
10.1007/s10483-013-1663-6
复制
发表时间：
2013-01
影响因子：
--
通讯作者：
Jin Li;Jianhua Huang
中科院分区：
文献类型：
--
作者：
Jin Li;Jianhua Huang
在Dirichlet边界条件下，研究了具有Hurst参数的二维随机不可压缩非牛顿流体在真圆柱分数布朗运动（FBM）驱动下的运动.利用空间微分算子谱的估计和解析数论中无穷重级数的恒等式，得到了随机非牛顿流体对应的随机卷积的存在性和正则性.在此基础上，对随机非牛顿系统，在参数H不作任何附加限制的情况下，得到了随机动力系统的温和解和随机吸引子的存在性。
A two-dimensional (2D) stochastic incompressible non-Newtonian fluid driven by the genuine cylindrical fractional Brownian motion (FBM) is studied with the Hurst parameterunder 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 withwithout any additional restriction on the parameterH.