Applied Mathematics and Mechanics

, Volume 34, Issue 2, pp 189–208 | Cite as

Dynamics of stochastic non-Newtonian fluids driven by fractional Brownian motion with Hurst parameter \(H \in \left( {\tfrac{1} {4},\tfrac{1} {2}} \right)\)

  • Jin Li (李 劲)Email author
  • Jian-hua Huang (黄建华)


A two-dimensional (2D) stochastic incompressible non-Newtonian fluid driven by the genuine cylindrical fractional Brownian motion (FBM) is studied with the Hurst parameter \(H \in \left( {\tfrac{1} {4},\tfrac{1} {2}} \right)\) 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 \(H \in \left( {\tfrac{1} {2},1} \right)\) without any additional restriction on the parameter H.

Key words

infinite-dimensional fractional Brownian motion (FBM) stochastic convolution stochastic non-Newtonian fluid random attractor 

Chinese Library Classification


2010 Mathematics Subject Classification

35Q35 35R60 60G22 37L55 


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Copyright information

© Shanghai University and Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Department of Mathematics and System ScienceNational University of Defense TechnologyChangshaP. R. China

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