Local well-posedness of the three dimensional compressible Euler–Poisson equations with physical vacuum

Abstract

This paper is concerned with the three dimensional compressible Euler–Poisson equations with moving physical vacuum boundary condition. This fluid system is usually used to describe the motion of a self-gravitating inviscid gaseous star. The local existence of classical solutions for initial data in certain weighted Sobolev spaces is established in the case that the adiabatic index satisfies 1<γ<3.