Interface Behavior of Compressible Navier--Stokes Equations with Vacuum

In this paper, we study a one-dimensional motion of viscous gas near vacuum with (or without) gravity. We are interested in the case that the gas is in contact with the vacuum at a finite interval. This is a free boundary problem for the one-dimensional isentropic Navier--Stokes equations, and the free boundaries are the interfaces separating the gas from vacuum, across which the density changes continuously. The regularity and behavior of the solutions near the interfaces and expanding rate of the interfaces are studied. Smoothness of the solutions is discussed. The uniqueness of the weak solutions to the free boundary problem is also proved.