Well-posedness of 1-D compressible Euler-Poisson equations with physical   vacuum
  This paper is concerned with the 1-D compressible Euler-Poisson equations with moving physical vacuum boundary condition. It is usually used to describe the motion of a self-gravitating inviscid gaseous star. The local well-posedness of classical solutions is established in the case of the adiabatic index $1<\gamma<3$. 
Xumin Gu and Zhen Lei
math.AP math-ph math.MP