  We consider a stochastic partial differential equation (SPDE) which describes
the velocity field of a viscous, incompressible non-Newtonian fluid subject to
a random force. Here the extra stress tensor of the fluid is given by a
polynomial of degree $p-1$ of the rate of strain tensor, while the colored
noise is considered as a random force. We investigate the existence and the
uniqueness of weak solutions to this SPDE.
