  We consider an evolution system modeling a flow of colloidal particles which
are suspended in an incompressible fluid and accounts for colloidal
crystallization. The system consists of the Navier-Stokes equations for the
volume averaged velocity coupled with the so-called Phase-Field Crystal
equation for the density deviation. Considering this system in a periodic
domain and assuming that the viscosity as well as the mobility depend on the
density deviation, we first prove the existence of a weak solution in dimension
three. Then, in dimension two, we establish the existence of a (unique) strong
solution.
