Artificial compressibility method for the Navier-Stokes-Maxwell-Stefan system

The Navier-Stokes-Maxwell-Stefan system describes the dynamics of an incompressible gaseous mixture in isothermal condition. In this paper we set up an artificial compressibility type approximation. In particular we focus on the existence of solution for the approximated system and the convergence to the incompressible case. The existence of the approximating system is proved by means of semidiscretization in time and by estimating the fractional time derivative.