An interesting problem in gas and fluid dynamics is to understand the behavior of vacuum states, namely the behavior of the system in the presence of vacuum. A particular interest is so called physical vacuum which naturally arises in physical problems. I'll report on a recent progress in a rigorous study of a physical vacuum. If time permits, I'll also discuss stability theory of Lane-Emden equilibrium stars under Euler-Poisson or Navier-Stokes-Poisson system.