  We perform mathematical anaysis of the biofilm development process. A model
describing biomass growth is proposed: It arises from coupling three parabolic
nonlinear equations: a biomass equation with degenerate and singular diffusion,
a nutrient tranport equation with a biomass-density dependent diffusion, and an
equation of the Navier-Stokes type, describing the fluid flow in which the
biofilm develops. This flow is subject to a biomass--density dependent
obstacle. The model is treated as a system of three inclusions, or variational
inequalities; the third one causes major difficulties for the system's
solvability. Our approach is based on the recent development of the theory on
Navier-Stokes variational inequalities.
