  We address the issue of existence of weak solutions for the non-homogeneous
Navier-Stokes system with Navier friction boundary conditions allowing the
presence of vacuum zones and assuming rough conditions on the data. We also
study the convergence, as the viscosity goes to zero, of weak solutions for the
non-homogeneous Navier-Stokes system with Navier friction boundary conditions
to the strong solution of the Euler equations with variable density, provided
that the initial data converge in $L^{2}$ to a smooth enough limit.
