  A 2D Stochastic incompressible non-Newtonian fluids driven by fractional
Bronwnian motion with Hurst parameter $H \in (1/2,1)$ is studied. The
Wiener-type stochastic integrals are introduced for infinite-dimensional
fractional Brownian motion. Four groups of assumptions, including the
requirement of Nuclear operator or Hilbert-Schmidt operator, are discussed. The
existence and regularity of stochastic convolution for the corresponding
additive linear stochastic equation are obtained under each group of
assumptions. Mild solution are then obtained for the non-Newtonian systems by
the modified fix point theorem in the selected intersection space. When the
domain is square, the random dynamical system generated by non-Newtonian
systems has a random attractor under some condition on the spectrum
distribution of the corresponding differential operator.
