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Dynamics of a 2D Stochastic non-Newtonian fluid driven by fractional Brownian motion

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  • A 2D Stochastic incompressible non-Newtonian fluid driven by fractional Brownian motion with Hurst index $H \in (\frac{1}{2},1)$ is studied. The Wiener-type stochastic integrals are introduced for infinite-dimensional fractional Brownian motion. Including the requirements of Nuclear and Hilbert-Schmidt operators, three kinds of condition, which ensure the existence and regularity of infinite-dimensional stochastic convolution for the corresponding additive linear stochastic equation, are summarized. Without the requirements of compact parameters, another condition is proposed for the existence and regularity of stochastic convolution. By any of the four kinds of condition, the existence and uniqueness of mild solution are obtained for the stochastic non-Newtonian fluid through a modified fixed point theorem in the selected intersection space. Existence of a random attractor is then obtained for the random dynamical system generated by non-Newtonian fluid.
    Mathematics Subject Classification: Primary: 35Q35, 35R60; Secondary: 60G22, 37L55.


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