The global solvability of the problem of nonlinear diffusion and slow convection in slightly compressible viscous fluid

The paper deals with Stokes system, corresponding to the motion of slightly compressible viscous fluid where kinematic viscous depends on the admixture concentration. The system also contains the convective diffusion equation. The article proves the existence of generalized solution of the initial-boundary problem for this system in the limited domain with the homogeneous Dirichlet condition for the fluid velocity and the homogeneous Neumann condition for the concentration of admixture on the boundary of domain.