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Dynamics of stochastic non-Newtonian fluids driven by fractional Brownian motion with Hurst parameter \(H \in (\tfrac 14,\tfrac 12)\). (English) Zbl 1457.76023

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

MSC:

76A05 Non-Newtonian fluids
76M35 Stochastic analysis applied to problems in fluid mechanics
60G22 Fractional processes, including fractional Brownian motion
60H30 Applications of stochastic analysis (to PDEs, etc.)
76D03 Existence, uniqueness, and regularity theory for incompressible viscous fluids
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