  In a previous work [math.AP/0305408] three of us have studied a nonlinear
parabolic equation arising in the mesoscopic modelling of concentrated
suspensions of particles that are subjected to a given time-dependent shear
rate. In the present work we extend the model to allow for a more physically
relevant situation when the shear rate actually depends on the macroscopic
velocity of the fluid, and as a feedback the macroscopic velocity is influenced
by the average stress in the fluid. The geometry considered is that of a planar
Couette flow. The mathematical system under study couples the one-dimensional
heat equation and a nonlinear Fokker-Planck type equation with nonhomogeneous,
nonlocal and possibly degenerate, coefficients. We show the existence and the
uniqueness of the global-in-time weak solution to such a system.
