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 $1<\gamma <3$.

92 pages. arXiv admin note: substantial text overlap with arXiv:1003.4721 by other authors

References in corpus (4)

• Global Solutions for Incompressible Viscoelastic Fluids
• Vanishing of vacuum states and blow-up phenomena of the compressible Navier-Stokes equations
• Uniform regularity and vanishing viscosity limit for the free surface Navier-Stokes equations
• On the Motion of Vortex Sheets with Surface Tension in the 3D Euler Equations with Vorticity

Cited by in corpus (1)

• Global Solutions to the Gas-Vacuum Interface Problem of Isentropic Compressible Inviscid Flows with Damping in Spherically Symmetric Motions and Physical Vacuum