Well-posedness of 1-D compressible Euler-Poisson equations with physical vacuum

TL;DR

This paper proves the local well-posedness of classical solutions for the 1-D compressible Euler-Poisson equations with physical vacuum boundary conditions, modeling self-gravitating gaseous stars for certain adiabatic indices.

Contribution

It establishes the first local well-posedness results for these equations with physical vacuum boundaries in the specified gamma range.

Findings

Proves local existence and uniqueness of solutions

Handles the physical vacuum boundary condition

Applicable for adiabatic index 1<γ<3

Abstract

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 $1<\gamma<3$.