A Class of Global Solutions to the Euler–Poisson System

Abstract

Using recent developments in the theory of globally defined expanding compressible gases, we construct a class of global-in-time solutions to the compressible 3-D Euler–Poisson system without any symmetry assumptions in both the gravitational and the plasma case. Our allowed range of adiabatic indices includes, but is not limited to all γ of the form γ=1+1n, n∈ N\ { 1 }. The constructed solutions have initially small densities, a compact support, and they stay close to Sideris affine solutions of the Euler system. As t→ ∞ the density scatters to zero and the support grows at a linear rate in t.