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 $1 < \gamma < 3$.