On the behavior of Kazhikov-Smagulov mass diffusion model for vanishing diffusion and viscosity coefficients

We consider the motion of a viscous incompressible fluid consisting of two components with a diffusion effect obeying Fick's law in R³.We prove that there exists a small time interval where the fluid variables converge uniformly as the viscosity and the diffusion coefficient tend to zero. In the limit, we find a non-homogeneous, non-viscous, incompressible fluid governed by an Euler-like system.