On the diffusion and slow convection in slightly compressible viscous fluid

We consider diffusion and slow convection of admixture in slightly compressible viscous fluid, described by the Stokes system, where viscous of fluid depends on the concentration of admixture. The Stokes system supplied by the diffusion equation with the convective term. We prove for this system the correctness of the initial-boundary problem in the limited domain with the homogeneous Dirichlet conditions for the fluid velocity and the homogeneous Neuman condition for the concentration of admixture on the boundary of domain.