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

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Abstract

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.

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Authors and Affiliations

  1. Department of Mathematics and System Science, National University of Defense Technology, Changsha, 410073, P. R. China

    Jin Li  (李 劲) & Jian-hua Huang  (黄建华)

Authors
  1. Jin Li  (李 劲)
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  2. Jian-hua Huang  (黄建华)
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Corresponding author

Correspondence to Jin Li  (李 劲).

Additional information

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)

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Li, J., Huang, Jh. Dynamics of stochastic non-Newtonian fluids driven by fractional Brownian motion with Hurst parameter \(H \in \left( {\tfrac{1} {4},\tfrac{1} {2}} \right)\) . Appl. Math. Mech.-Engl. Ed. 34, 189–208 (2013). https://doi.org/10.1007/s10483-013-1663-6

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  • DOI: https://doi.org/10.1007/s10483-013-1663-6

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